Segment Occurrences

You are given two strings s and t, both consisting only of lowercase Latin letters.

The substring s[l..r] is the string which is obtained by taking characters s_l, s_{l + 1}, ..., s_r without changing the order.

Each of the occurrences of string a in a string b is a position i (1 ≤ i ≤ |b| - |a| + 1) such that b[i..i + |a| - 1] = a (|a| is the length of string a).

You are asked q queries: for the i-th query you are required to calculate the number of occurrences of string t in a substring s[l_i..r_i].

Input

The first line contains three integer numbers n, m and q (1 ≤ n, m ≤ 10^3, 1 ≤ q ≤ 10^5) — the length of string s, the length of string t and the number of queries, respectively.

The second line is a string s (|s| = n), consisting only of lowercase Latin letters.

The third line is a string t (|t| = m), consisting only of lowercase Latin letters.

Each of the next q lines contains two integer numbers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n) — the arguments for the i-th query.

Output

Print q lines — the i-th line should contain the answer to the i-th query, that is the number of occurrences of string t in a substring s[l_i..r_i].

Examples

Input

10 3 4 codeforces for 1 3 3 10 5 6 5 7

Output

0 1 0 1

Input

15 2 3 abacabadabacaba ba 1 15 3 4 2 14

Output

4 0 3

Input

3 5 2 aaa baaab 1 3 1 1

Output

0 0

Note

In the first example the queries are substrings: "cod", "deforces", "fo" and "for", respectively.

inputFormat

Input

The first line contains three integer numbers n, m and q (1 ≤ n, m ≤ 10^3, 1 ≤ q ≤ 10^5) — the length of string s, the length of string t and the number of queries, respectively.

The second line is a string s (|s| = n), consisting only of lowercase Latin letters.

The third line is a string t (|t| = m), consisting only of lowercase Latin letters.

Each of the next q lines contains two integer numbers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n) — the arguments for the i-th query.

outputFormat

Output

Print q lines — the i-th line should contain the answer to the i-th query, that is the number of occurrences of string t in a substring s[l_i..r_i].

Examples

Input

10 3 4 codeforces for 1 3 3 10 5 6 5 7

Output

0 1 0 1

Input

15 2 3 abacabadabacaba ba 1 15 3 4 2 14

Output

4 0 3

Input

3 5 2 aaa baaab 1 3 1 1

Output

0 0

Note

In the first example the queries are substrings: "cod", "deforces", "fo" and "for", respectively.

样例

15 2 3
abacabadabacaba
ba
1 15
3 4
2 14

4
0
3

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