Isomorphic Strings

3000ms

262144K

Description:

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(s_i) = t_i. Formally:

f(s_i) = t_i for any index i,
for any character $\text{[math]}$ there is exactly one character $\text{[math]}$ that f(x) = y,
for any character $\text{[math]}$ there is exactly one character $\text{[math]}$ 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: x_i, y_i and len_i (1 ≤ x_i, y_i ≤ n, 1 ≤ len_i ≤ n - max(x_i, y_i) + 1) — the description of the pair of the substrings to check.

Output:

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

Sample Input:

Sample Output:

YES
YES
NO
YES

Note:

The queries in the example are following:

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

Informação

Provedor Codeforces

Código CF985F