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 sys

def solve(ist):
    _ = ist.next_int()
    _ = ist.next_int()
    q = ist.next_int()

    s = ist.next()
    t = ist.next()

    counts = [0 for _ in xrange(len(s) + 1)]
    for i in xrange(1, len(s) + 1):
        counts[i] = counts[i - 1]
        if s[i - 1: i - 1 + len(t)] == t:
            counts[i] += 1

    queries = [(ist.next_int(), ist.next_int()) for _ in xrange(q)]
    for l, r in queries:
        if r - l + 1 < len(t):
            ans = 0
        else:
            ans = counts[r - len(t) + 1] - counts[l - 1]
        print ans

# -----------------------------------------------------------------------------
class InputStream(object):
    @staticmethod  # use as decorator
    def input_generator(fd):
        for line in fd:
            for t in line.split():
                yield t

    def __init__(self, fd):
        self.stream = InputStream.input_generator(fd)

    def __iter__(self):
        return self

    def next(self):
        return next(self.stream)

    def next_int(self):
        return int(self.next())

    def next_float(self):
        return float(self.next())


def main():
    if len(sys.argv) > 1:
        fd = open(sys.argv[1], "r")
    else:
        fd = sys.stdin

    ist = InputStream(fd)
    while True:
        try:
            solve(ist)
        except StopIteration:
            break


if __name__ == "__main__":
    main()
