4131번 - Modulo Solitaire

Modulo Solitaire is a game that can be played when you are bored. You can even play it without a phone, just on paper. First, you pick a number m. Then you pick two sequences of numbers ai and bi. Finally, you pick a starting number s0. Now, your goal is to go from s0 to 0 in as few moves as possible. In each move, you choose an i, then multiply your current number by ai, add bi to it, and reduce the result modulo m. That is, sj = (sj-1 * aij + bij) % m.

The first line of input contains three integers 0 < m ≤ 1000000, 0 ≤ n ≤ 10, and 0 < s0 < m. The next n lines each contain two integers, a pair 0 ≤ ai ≤ 1000000000 and 0 ≤ bi ≤ 1000000000.

Output a single integer, the shortest number of moves needed to reach 0 starting from s0. If it is not possible to reach 0 in any number of moves, output -1.