【cf464C】Substitutes in Number

2014年9月8日1,5930

Andrew and Eugene are playing a game. Initially, Andrew has string s, consisting of digits. Eugene sends Andrew multiple queries of type “di → ti“, that means “replace all digits di in string s with substrings equal to ti“. For example, if s = 123123, then query “2 → 00” transforms s to 10031003, and query “3 → ” (“replace 3 by an empty string”) transforms it to s = 1212. After all the queries Eugene asks Andrew to find the remainder after division of number with decimal representation equal to s by 1000000007 (109 + 7). When you represent s as a decimal number, please ignore the leading zeroes; also if s is an empty string, then it’s assumed that the number equals to zero.

Andrew got tired of processing Eugene’s requests manually and he asked you to write a program for that. Help him!

Input

The first line contains string s (1 ≤ |s| ≤ 105), consisting of digits — the string before processing all the requests.

The second line contains a single integer n (0 ≤ n ≤ 105) — the number of queries.

The next n lines contain the descriptions of the queries. The i-th query is described by string “di->ti“, where di is exactly one digit (from 0 to 9), ti is a string consisting of digits (ti can be an empty string). The sum of lengths of ti for all queries doesn’t exceed 105. The queries are written in the order in which they need to be performed.

Output

Print a single integer — remainder of division of the resulting number by 1000000007 (109 + 7).

Sample test(s)
input

output

input

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input

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output

Note

Note that the leading zeroes are not removed from string s after the replacement (you can see it in the third sample).

 

题解

简直神题。。。orz无数次jiry_2神的代码才领悟的

题意给定一个数字串,每次把某个数字变成一串数字。。。

最后把数字串当作一个数字,输出其mod1000000007的值

用to[i]表示第i个数字变成的数值(mod),l[i]表示该数字的位数

然后倒序处理这俩个数组,处理过程中使用快速幂

还要注意在变化过程中l[i]可能非常大

这时根据费马小定理,可以取模1000000006

因为a^(p-1) mod p=a^0 mod p