cf 985 F. Isomorphic Strings 字符串hash

F. Isomorphic Strings

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a string s of length n consisting of lowercase English letters.

For two given strings s and t, say S is the set of distinct characters of s and T is the set of distinct characters of t. The strings s and t are isomorphic if their lengths are equal and there is a one-to-one mapping (bijection) f between S and T for which f(si) = ti. Formally:

1. f(si) = ti for any index i,
2. for any character  there is exactly one character  that f(x) = y,
3. for any character  there is exactly one character  that f(x) = y.

For example, the strings "aababc" and "bbcbcz" are isomorphic. Also the strings "aaaww" and "wwwaa" are isomorphic. The following pairs of strings are not isomorphic: "aab" and "bbb", "test" and "best".

You have to handle m queries characterized by three integers x, y, len (1 ≤ x, y ≤ n - len + 1). For each query check if two substrings s[x... x + len - 1] and s[y... y + len - 1] are isomorphic.

Input

The first line contains two space-separated integers n and m (1 ≤ n ≤ 2·105, 1 ≤ m ≤ 2·105) — the length of the string s and the number of queries.

The second line contains string s consisting of n lowercase English letters.

The following m lines contain a single query on each line: xi, yi and leni (1 ≤ xi, yi ≤ n, 1 ≤ leni ≤ n - max(xi, yi) + 1) — the description of the pair of the substrings to check.

Output

For each query in a separate line print "YES" if substrings s[xi... xi + leni - 1] and s[yi... yi + leni - 1] are isomorphic and "NO" otherwise.

Example

input

Copy

7 4
abacaba
1 1 1
1 4 2
2 1 3
2 4 3

output

Copy

YES
YES
NO
YES

Note

The queries in the example are following:

1. substrings "a" and "a" are isomorphic: f(a) = a;
2. substrings "ab" and "ca" are isomorphic: f(a) = c, f(b) = a;
3. substrings "bac" and "aba" are not isomorphic since f(b) and f(c) must be equal to a at same time;
4. substrings "bac" and "cab" are isomorphic: f(b) = c, f(a) = a, f(c) = b.

注意素數的選取，必要時雙hash

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int M=200005;
const ll MOD=1e9+7;
char s[M];
ll px[M],X=107,h[26][M];
int main()
{
    int n,m;
    scanf("%d%d%s",&n,&m,s+1);
    px[0]=1;
    for(int i=1;i<=n;i++)px[i]=px[i-1]*X%MOD;
    for(int i=0;i<26;i++)
    {
        for(int j=1;j<=n;j++)h[i][j]=(h[i][j-1]*X+ll(s[j]=='a'+i))%MOD;
    }
    while(m--)
    {
        int x,y,l;
        scanf("%d%d%d",&x,&y,&l);
        vector<int> p,q;
        for(int i=0;i<26;i++)
        {
            q.push_back((h[i][x+l-1]-px[l]*h[i][x-1]%MOD+MOD)%MOD);
            p.push_back((h[i][y+l-1]-px[l]*h[i][y-1]%MOD+MOD)%MOD);
        }
        sort(p.begin(),p.end());
        sort(q.begin(),q.end());
        printf("%s\n",p==q?"YES":"NO");
    }
    return 0;
}