Drain Pipes

Yeongman's house is so old that water keeps leaking from the toilet. Fed up with it, Yeongman decides to fix the drainage himself by joining the spare pipes he has at home.

Cutting a pipe costs far too much, so he must join the leftover pipes as they are to build a pipe of exactly length $x$, without cutting any of them. Given the length and quantity of each pipe he owns, count the number of ways to join pipes into a total length of $x$. The order in which pipes are joined does not matter.

The first line contains the number of pipe types $N$ and the desired total length $x$. ($1 \le N \le 100$, $1 \le x \le 10000$)

Each of the following $N$ lines contains a pipe length $L_i$ and its quantity $C_i$, separated by a space. ($0 < L_i \le x$, $0 < C_i \le 100$) The pipes are given in ascending order of length, and no two types share the same length.

Print the number of ways to build a joined pipe of exactly length $x$. The answer never exceeds $2147483647$.