A8914 | Coin Troubles

In the Isle of Guernsey there are $n$ different types of coins. For each $i$ $(1<=i<=n)$ , coin of type $i$ is worth $a_{i}$ cents. It is possible that $a_{i}=a_{j}$ for some $i$ and $j$ $(i≠j)$ .

Bessie has some set of these coins totaling $t$ cents. She tells Jessie $q$ pairs of integers. For each $i$ $(1<=i<=q)$ , the pair $b_{i},c_{i}$ tells Jessie that Bessie has a strictly greater number of coins of type $b_{i}$ than coins of type $c_{i}$ . It is known that all $b_{i}$ are distinct and all $c_{i}$ are distinct.

Help Jessie find the number of possible combinations of coins Bessie could have. Two combinations are considered different if there is some $i$ $(1<=i<=n)$ , such that the number of coins Bessie has of type $i$ is different in the two combinations. Since the answer can be very large, output it modulo $1000000007$ $(10^{9}+7)$ .

If there are no possible combinations of coins totaling $t$ cents that satisfy Bessie's conditions, output 0.

The first line contains three space-separated integers, $n,q$ and $t$ $(1<=n<=300; 0<=q<=n; 1<=t<=10^{5})$ . The second line contains $n$ space separated integers, $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=10^{5})$ . The next $q$ lines each contain two distinct space-separated integers, $b_{i}$ and $c_{i}$ $(1<=b_{i},c_{i}<=n; b_{i}≠c_{i})$ .

It's guaranteed that all $b_{i}$ are distinct and all $c_{i}$ are distinct.

A single integer, the number of valid coin combinations that Bessie could have, modulo $1000000007$ $(10^{9}+7)$ .