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.
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;

public class SegmentOccurrences {

    static String  P, S;
    static Scanner scanner = new Scanner(System.in);
    static int n, m, q;
    static int a, b,  length;

    public static void main(String[] args) {

        n = scanner.nextInt();
        m = scanner.nextInt();
        q = scanner.nextInt();

        S = scanner.next();
        P = scanner.next();

        
        long occurrences;
        List<Integer> list = KMP(S, P);
        for(int i = 0; i < q; ++i){

            a =  scanner.nextInt() - 1;
            b =  scanner.nextInt();
            length = b - a;
            if(b - a < P.length()){
                System.out.println(0);
                continue;
            }

            occurrences = list.stream().filter(x -> (x >= a) && x <= (b - P.length())).count();
            System.out.println(occurrences);

        }
        
        
    }
    


    static List<Integer> KMP(String T, String P){

        String S = P + '$' + T;
        int[] prefix = prefix(S);

        List<Integer> result = new LinkedList<>();
        
        for(int i = P.length() + 1; i < S.length(); ++i)
            if(prefix[i] == P.length())
                result.add(i - 2 * P.length());

        return result;
    }

    static int[] prefix(String P)
    {

        int[] prefix = new int[P.length()];
        int border = 0; prefix[0] = 0;

        for(int i = 1; i < P.length(); ++i){


            while(border > 0 && P.charAt(i) != P.charAt(border))
                border = prefix[border - 1];

            if(P.charAt(i) == P.charAt(border))
                border = border + 1;

            else
                border = 0;

            prefix[i] = border;

        }


        return prefix;

    } 





}