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#F0922. Math, math everywhere

    ID: 928 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 10 上传者: 标签>枚举动态规划数学折半搜索数论算法思想搜索挑战难度共享题库Codeforces英文题面题目来源题面语言

Math, math everywhere

题目描述

G. Math, math everywhere
time limit per test
5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

If you have gone that far, you'll probably skip unnecessary legends anyway...

You are given a binary string and an integer . Find the number of integers k, 0≤k<N, such that for all i=0, 1, ..., m-1

Print the answer modulo 109+7.
Input

In the first line of input there is a string s consisting of 0's and 1's (1≤|s|≤40).

In the next line of input there is an integer n (1≤n≤5·105).

Each of the next n lines contains two space-separated integers pi, αi (1≤pi,αi≤109, pi is prime). All pi are distinct.

Output

A single integer− the answer to the problem.

Examples
Input
1
2
2 1
3 1
Output
2
Input
01
2
3 2
5 1
Output
15
Input
1011
1
3 1000000000
Output
411979884

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 357 题。保留原作者与原赛事署名。