# Codeforces Round #598 (Div. 3)

## A. Payment Without Change

time limit per test1 second memory limit per test256 megabytes

You have a coins of value n and b coins of value 1. You always pay in exact change, so you want to know if there exist such x and y that if you take x$$(0 \le x \le a)$$ coins of value n and y $$(0 \le y \le b)$$coins of value 1, then the total value of taken coins will be S.

You have to answer q independent test cases.

Input

The first line of the input contains one integer q $$(1 \le q \le 10^4)$$ — the number of test cases. Then q test cases follow.

The only line of the test case contains four integers a, b, n and S $$(1 \le a, b, n, S \le 10^9)$$— the number of coins of value n, the number of coins of value 1, the value n and the required total value.

Output

For the i-th test case print the answer on it — YES (without quotes) if there exist such x and y that if you take x coins of value n and y coins of value 1, then the total value of taken coins will be S, and NO otherwise.

You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).

Exampleinput

4
1 2 3 4
1 2 3 6
5 2 6 27
3 3 5 18

output

YES
NO
NO
YES

#### 签到

#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const int maxn=(int)2e5+100;
const int mod=(int)1e9+7;
void solve(){
ll a,b,n,s;cin>>a>>b>>n>>s;
if(a*n+b<s) return (void)puts("NO");
ll tmp=s/n;
if(tmp<=a) s%=n;
else s-=a*n;
return (void)puts(s<=b?"YES":"NO");
}
int main(){
int T;cin>>T;
while(T--) solve();
}


## B. Minimize the Permutation

time limit per test1 second memory limit per test256 megabytes

You are given a permutation of length n. Recall that the permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2, 3, 1, 5, 4] is a permutation, but [1, 2, 2] is not a permutation (2 appears twice in the array) and [1, 3, 4] is also not a permutation (n=3 but there is 4 in the array).

You can perform at most n-1 operations with the given permutation (it is possible that you don’t perform any operations at all). The i-th operation allows you to swap elements of the given permutation on positions i and i+1. Each operation can be performed at most once. The operations can be performed in arbitrary order.

Your task is to find the lexicographically minimum possible permutation obtained by performing some of the given operations in some order.

You can see the definition of the lexicographical order in the notes section.

You have to answer q independent test cases.

For example, let’s consider the permutation [5, 4, 1, 3, 2]. The minimum possible permutation we can obtain is [1, 5, 2, 4, 3] and we can do it in the following way:

1. perform the second operation (swap the second and the third elements) and obtain the permutation [5, 1, 4, 3, 2];
2. perform the fourth operation (swap the fourth and the fifth elements) and obtain the permutation [5, 1, 4, 2, 3];
3. perform the third operation (swap the third and the fourth elements) and obtain the permutation [5, 1, 2, 4, 3].
4. perform the first operation (swap the first and the second elements) and obtain the permutation [1, 5, 2, 4, 3];

Another example is [1, 2, 4, 3]. The minimum possible permutation we can obtain is [1, 2, 3, 4] by performing the third operation (swap the third and the fourth elements).

Input

The first line of the input contains one integer q $$(1 \le q \le 100)$$ — the number of test cases. Then q test cases follow.

The first line of the test case contains one integer n $$(1 \le n \le 100)$$ — the number of elements in the permutation.

The second line of the test case contains n distinct integers from 1 to n — the given permutation.

Output

For each test case, print the answer on it — the lexicograhically minimum possible permutation obtained by performing some of the given operations in some order.

Exampleinput

4
5
5 4 1 3 2
4
1 2 4 3
1
1
4
4 3 2 1

output

1 5 2 4 3
1 2 3 4
1
1 4 3 2 

Note

Recall that the permutation p of length n is lexicographically less than the permutation q of length n if there is such index $$i \le n$$that for all j from 1 to i – 1 the condition $$p_j = q_j$$ is satisfied, and $$p_i < q_i$$. For example:

• p = [1, 3, 5, 2, 4] is less than q = [1, 3, 5, 4, 2] (such i=4 exists, that $$p_i < q_i$$ and for each j < i holds $$p_j = q_j$$),
• p = [1, 2] is less than q = [2, 1] (such i=1 exists, that $$p_i < q_i$$ and for each j < i holds $$p_j = q_j$$).

#### 模拟题，暴力

#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const int maxn=(int)2e5+100;
const int mod=(int)1e9+7;
int n,a[maxn];
void solve(){
scanf("%d",&n);
rep(i,1,n) scanf("%d",&a[i]);
int vis={0,};
rep(now,1,n){
rep(i,1,n) if(a[i]==now){
dep(j,i-1,1){
if(!vis[j]&&a[j]>a[j+1]){
vis[j]=1;
swap(a[j],a[j+1]);
}
else break;
}
}
}
rep(i,1,n) printf(i==n?"%d\n":"%d ",a[i]);
}
int main(){
int T;cin>>T;
while(T--) solve();
}


## C. Platforms Jumping

time limit per test1 second memory limit per test256 megabytes

There is a river of width n. The left bank of the river is cell 0 and the right bank is cell n + 1 (more formally, the river can be represented as a sequence of n + 2 cells numbered from 0 to n + 1). There are also m wooden platforms on a river, the i-th platform has length$$c_i$$ (so the i-th platform takes$$c_i$$consecutive cells of the river). It is guaranteed that the sum of lengths of platforms does not exceed n.

You are standing at 0 and want to reach n+1 somehow. If you are standing at the position x, you can jump to any position in the range [x + 1; x + d]. However you don’t really like the water so you can jump only to such cells that belong to some wooden platform. For example, if d=1, you can jump only to the next position (if it belongs to the wooden platform). You can assume that cells 0 and n+1 belong to wooden platforms.

You want to know if it is possible to reach n+1 from 0 if you can move any platform to the left or to the right arbitrary number of times (possibly, zero) as long as they do not intersect each other (but two platforms can touch each other). It also means that you cannot change the relative order of platforms.

Note that you should move platforms until you start jumping (in other words, you first move the platforms and then start jumping).

For example, if n=7, m=3, d=2 and c = [1, 2, 1], then one of the ways to reach 8 from 0 is follow:

The first example: n=7.

Input

The first line of the input contains three integers n, m and d $$(1 \le n, m, d \le 1000, m \le n)$$— the width of the river, the number of platforms and the maximum distance of your jump, correspondingly.

The second line of the input contains m integers $$c_1, c_2, \dots, c_m (1 \le c_i \le n, \sum\limits_{i=1}^{m} c_i \le n)$$, where c_i is the length of the i-th platform.

Output

If it is impossible to reach n+1 from 0, print NO in the first line. Otherwise, print YES in the first line and the array a of length n in the second line — the sequence of river cells (excluding cell 0 and cell n + 1).

If the cell i does not belong to any platform, a_i should be 0. Otherwise, it should be equal to the index of the platform (1-indexed, platforms are numbered from 1 to m in order of input) to which the cell i belongs.

Note that all$$a_i$$ equal to 1 should form a contiguous subsegment of the array a of length $$c_1$$, all $$a_i$$ equal to 2 should form a contiguous subsegment of the array a of length $$c_2$$, …, all $$a_i$$ equal to m should form a contiguous subsegment of the array a of length c_m. The leftmost position of 2 in a should be greater than the rightmost position of 1, the leftmost position of 3 in a should be greater than the rightmost position of 2, …, the leftmost position of m in a should be greater than the rightmost position of m-1.

See example outputs for better understanding.

Examplesinput

7 3 2
1 2 1

output

YES
0 1 0 2 2 0 3 

input

10 1 11
1

output

YES
0 0 0 0 0 0 0 0 0 1 

input

10 1 5
2

output

YES
0 0 0 0 1 1 0 0 0 0 

Note

Consider the first example: the answer is [0, 1, 0, 2, 2, 0, 3]. The sequence of jumps you perform is$$0 \rightarrow 2 \rightarrow 4 \rightarrow 5 \rightarrow 7 \rightarrow 8$$.

Consider the second example: it does not matter how to place the platform because you always can jump from 0 to 11.

Consider the third example: the answer is [0, 0, 0, 0, 1, 1, 0, 0, 0, 0]. The sequence of jumps you perform is $$0 \rightarrow 5 \rightarrow 6 \rightarrow 11$$.

#### 模拟题，签到

#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const int maxn=(int)2e5+100;
const int mod=(int)1e9+7;
int n,m,d,c[maxn],sum;
int main(){
scanf("%d%d%d",&n,&m,&d);
rep(i,1,m) scanf("%d",&c[i]),sum+=c[i];
if(sum+(m+1)*(d-1)<n) return puts("NO"),0;
puts("YES");
n=n-sum+1;
rep(i,1,m+1){
int tmp=min(d,n);
rep(j,1,tmp-1) printf("0 ");
rep(j,1,c[i]) printf("%d ",i);
n-=tmp-1;
}
}


## D. Binary String Minimizing

time limit per test1 second memory limit per test256 megabytes

You are given a binary string of length n (i. e. a string consisting of n characters ‘0’ and ‘1’).

In one move you can swap two adjacent characters of the string. What is the lexicographically minimum possible string you can obtain from the given one if you can perform no more than k moves? It is possible that you do not perform any moves at all.

Note that you can swap the same pair of adjacent characters with indices i and i+1 arbitrary (possibly, zero) number of times. Each such swap is considered a separate move.

You have to answer q independent test cases.

Input

The first line of the input contains one integer q $$(1 \le q \le 10^4)$$ — the number of test cases.

The first line of the test case contains two integers n and k $$(1 \le n \le 10^6, 1 \le k \le n^2)$$ — the length of the string and the number of moves you can perform.

The second line of the test case contains one string consisting of n characters ‘0’ and ‘1’.

It is guaranteed that the sum of n over all test cases does not exceed $$10^6 (\sum n \le 10^6)$$.

Output

For each test case, print the answer on it: the lexicographically minimum possible string of length n you can obtain from the given one if you can perform no more than k moves.

Exampleinput

3
8 5
11011010
7 9
1111100
7 11
1111100

output

01011110
0101111
0011111

Note

In the first example, you can change the string as follows: $$1\underline{10}11010 \rightarrow \underline{10}111010 \rightarrow 0111\underline{10}10 \rightarrow 011\underline{10}110 \rightarrow 01\underline{10}1110 \rightarrow 01011110$$.

In the third example, there are enough operations to make the string sorted.

#### 比c题简单，模拟就行了

#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const int maxn=(int)1e6+100;
const int mod=(int)1e9+7;
char s[maxn];
void solve(){
ll n,k;scanf("%lld%lld%s",&n,&k,s+1);
ll cnt=0,ans=0,tmp;
rep(i,1,n){
if(s[i]=='0'){
cnt++;tmp=i-cnt;ans+=tmp;
}
if(ans>k){
rep(j,1,cnt-1) printf("0");
ll pos=i-(k-(ans-tmp));
rep(j,cnt,pos-1) printf("1");
printf("0");
rep(j,pos+1,i) printf("1");
rep(j,i+1,n) printf("%c",s[j]);
puts("");return;
}
}
sort(s+1,s+1+n);
printf("%s\n",s+1);
}
int main(){
int T;cin>>T;
while(T--) solve();
}


## E. Yet Another Division Into Teams

time limit per test2 seconds memory limit per test256 megabytes

There are n students at your university. The programming skill of the i-th student is $$a_i$$. As a coach, you want to divide them into teams to prepare them for the upcoming ICPC finals. Just imagine how good this university is if it has $$2 \cdot 10^5$$students ready for the finals!

Each team should consist of at least three students. Each student should belong to exactly one team. The diversity of a team is the difference between the maximum programming skill of some student that belongs to this team and the minimum programming skill of some student that belongs to this team (in other words, if the team consists of k students with programming skills $$a[i_1], a[i_2], \dots, a[i_k]$$, then the diversity of this team is $$\max\limits_{j=1}^{k} a[i_j] – \min\limits_{j=1}^{k} a[i_j])$$.

The total diversity is the sum of diversities of all teams formed.

Your task is to minimize the total diversity of the division of students and find the optimal way to divide the students.

Input

The first line of the input contains one integer n $$(3 \le n \le 2 \cdot 10^5)$$ — the number of students.

The second line of the input contains n integers $$a_1, a_2, \dots, a_n (1 \le a_i \le 10^9)$$, where $$a_i$$ is the programming skill of the i-th student.

Output

In the first line print two integers res and k — the minimum total diversity of the division of students and the number of teams in your division, correspondingly.

In the second line print n integers $$t_1, t_2, \dots, t_n (1 \le t_i \le k)$$, where$$t_i$$ is the number of team to which the i-th student belong.

If there are multiple answers, you can print any. Note that you don’t need to minimize the number of teams. Each team should consist of at least three students.

Examplesinput

5
1 1 3 4 2

output

3 1
1 1 1 1 1 

input

6
1 5 12 13 2 15

output

7 2
2 2 1 1 2 1 

input

10
1 2 5 129 185 581 1041 1909 1580 8150

output

7486 3
3 3 3 2 2 2 2 1 1 1 

Note

In the first example, there is only one team with skills [1, 1, 2, 3, 4] so the answer is 3. It can be shown that you cannot achieve a better answer.

In the second example, there are two teams with skills [1, 2, 5] and [12, 13, 15] so the answer is 4 + 3 = 7.

In the third example, there are three teams with skills [1, 2, 5], [129, 185, 581, 1041] and [1580, 1909, 8150] so the answer is 4 + 912 + 6570 = 7486.

#### 裸的DP，一个队伍的人数不会超过5个(因为大于5的话就可以分为超过一个队，肯定更优)，所以每个人只要考虑之前5个人就好啦，效率$$O(n)$$

#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const int maxn=(int)2e5+100;
const int mod=(int)1e9+7;
int n,cnt,ans[maxn];
pair<ll,int> a[maxn],dp[maxn];
int main(){
scanf("%d",&n);
rep(i,1,n) scanf("%lld",&a[i].first),a[i].second=i,dp[i]={4e18,0};
sort(a+1,a+1+n);
rep(i,1,n) rep(j,max(0,i-5),i-3)
dp[i]=min(dp[i],{dp[j].first+a[i].first-a[j+1].first,j});
for(int i=n;i;i=dp[i].second){
++cnt;
rep(j,dp[i].second+1,i) ans[a[j].second]=cnt;
}
printf("%lld %d\n",dp[n].first,cnt);
rep(i,1,n) printf("%d ",ans[i]);
}


## F. Equalizing Two Strings

time limit per test1 second memory limit per test256 megabytes

You are given two strings s and t both of length n and both consisting of lowercase Latin letters.

In one move, you can choose any length len from 1 to n and perform the following operation:

• Choose any contiguous substring of the string s of length len and reverse it;
• at the same time choose any contiguous substring of the string t of length len and reverse it as well.

Note that during one move you reverse exactly one substring of the string s and exactly one substring of the string t.

Also note that borders of substrings you reverse in s and in t can be different, the only restriction is that you reverse the substrings of equal length. For example, if len=3 and n=5, you can reverse $$s[1 \dots 3] and t[3 \dots 5], s[2 \dots 4] and t[2 \dots 4]$$, but not $$s[1 \dots 3] and t[1 \dots 2]$$.

Your task is to say if it is possible to make strings s and t equal after some (possibly, empty) sequence of moves.

You have to answer q independent test cases.

Input

The first line of the input contains one integer q $$(1 \le q \le 10^4)$$ — the number of test cases. Then q test cases follow.

The first line of the test case contains one integer n $$(1 \le n \le 2 \cdot 10^5)$$— the length of s and t.

The second line of the test case contains one string s consisting of n lowercase Latin letters.

The third line of the test case contains one string t consisting of n lowercase Latin letters.

It is guaranteed that the sum of n over all test cases does not exceed $$2 \cdot 10^5 (\sum n \le 2 \cdot 10^5)$$.

Output

For each test case, print the answer on it — “YES” (without quotes) if it is possible to make strings s and t equal after some (possibly, empty) sequence of moves and “NO” otherwise.

Exampleinput

4
4
abcd
abdc
5
ababa
baaba
4
asdf
asdg
4
abcd
badc

output

NO
YES
NO
YES

#### 首先判断掉字母不匹配的情况，显然是NO； 再考虑某个字母出现次数大于1的情况，这种情况显然是YES，因为我们可以使得s和t都变成sorted的字符串，显然我们可以通过那个个数大于1的字母调整数量使得两个串的操作数相等； 那么现在只剩下一种情况，就是所有字母出现次数都小于等于1，此时只需要判断s和t中的逆序对数量的奇偶性是否相等就好啦

#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const int maxn=(int)2e5+100;
const int mod=(int)1e9+7;
int n,num1,num2;
char s[maxn],t[maxn];
void solve(){
scanf("%d%s%s",&n,s+1,t+1);
rep(i,0,29) num1[i]=num2[i]=0;
int c1=0,c2=0,flag=0;
rep(i,1,n) num1[s[i]-'a']++;
rep(i,1,n) num2[t[i]-'a']++;
rep(i,0,25){
if(num1[i]!=num2[i]) return (void)puts("NO");
if(num1[i]>1) flag=1;
}
if(flag) return (void)puts("YES");
rep(i,1,n) rep(j,1,i-1){
c1+=(s[j]>s[i]);
c2+=(t[j]>t[i]);
}
return (void)puts((c1&1)==(c2&1)?"YES":"NO");
}
int main(){
int T;cin>>T;
while(T--) solve();
}