Farmer John is hiring a new herd leader for his cows. To that end, he has interviewed $N$ ($2 \leq N \leq 10^9$) cows for the position. After each interview, he assigned an integer "cowmpetency" score to the candidate ranging from $1$ to $C$ ($1 \leq C \leq 10^4$) that is correlated with their leadership abilities.

Because he has interviewed so many cows, Farmer John has forgotten all of their cowmpetency scores. However, he does remembers $Q$ ($1 \leq Q \leq \min(N - 1, 100)$) pairs of numbers $(a_i, h_i)$ where cow $h_i$ was the first cow with a strictly greater cowmpetency score than cows $1$ through $a_i$ (so $1 \leq a_i < h_i \leq N$).

Farmer John now tells you the $Q$ pairs of $(a_i, h_i)$. Help him count how many sequences of cowmpetency scores are consistent with this information! It is guaranteed that there is at least one such sequence. Because this number may be very large, output its value modulo $10^9 + 7$.

SAMPLE INPUT:

6 2 3
2 3
4 5

SAMPLE OUTPUT:

6

The following six sequences are the only ones consistent with what Farmer John remembers:

1 1 2 1 3 1
1 1 2 1 3 2
1 1 2 1 3 3
1 1 2 2 3 1
1 1 2 2 3 2
1 1 2 2 3 3

SAMPLE INPUT:

10 1 20
1 3

SAMPLE OUTPUT:

399988086

Make sure to output the answer modulo $10^9+7$.

Problem credits: Suhas Nagar