Given two integers a and b (1 <= a, b <= 1e5). m = 1e9 + 7.

There will be up to 1e5 steps. In each step-
1. Two integers t (1 <= t <= 2) and c (1 <= c <= 1e5) are given. If t = 1, multiply a by c. Else if t = 2, multiply b by c.
2. Find the value of (a % b) % m.

Note that, a or b may be changed after each step.

btw, it's not any OJ problem. I'm just interested about the solution.