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C. Coin Troubles

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn 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.

Input

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.

Output

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

Examples

Input

4 2 17

3 1 2 5

4 2

3 4

Output

3

Input

3 2 6

3 1 1

1 2

2 3

Output

0

Input

3 2 10

1 2 3

1 2

2 1

Output

0

Note

For the first sample, the following 3 combinations give a total of 17 cents and satisfy the given conditions: {0 *of* *type* 1, 1 *of* *type* 2, 3 *of* *type* 3, 2 *of* *type* 4}, {0, 0, 6, 1}, {2, 0, 3, 1}.

No other combinations exist. Note that even though 4 occurs in both *b*_{i} and *c*_{i}, the problem conditions are still satisfied because all *b*_{i} are distinct and all *c*_{i} are distinct.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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