Time Limit: 2 Seconds
Memory Limit: 65536 KB
There is a digit string S with infinite length. In addition, S is periodic and it can be formed by concatenating infinite repetitions of a base string P. For example, if P = 3423537, then S = 3423537342353734235373423537...
Let's define the alternating sum on substrings of S. Assume Sl..r is a substring of S from index l to index r (all indexes are 1-based), then the alternating sum of Sl..r is:
For example, S2..10 = 423537342, then G(2, 10) = 4 - 2 + 3 - 5 + 3 - 7 + 3 - 4 + 2 = -3.
Now, you are given the base string P and you have to do many operations. There are only two kinds of operations:
For each second operation, you should output the sum modulo 109 + 7.
There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:
The first line contains a digit string P (1 <= length(P) <= 100000).
The second line contains an integer Q (1 <= Q <= 100000) indicating the number of operations. Each of the following Q lines is an operation in such format: