Wolves

Wolves appear on the road where Yeongseon is standing, so she is working out carefully where they can be.

The road is divided into $N$ sections numbered $0$ through $N-1$. A section holds at most one wolf.

Yeongseon knows $M$ pieces of information about the wolves. Each piece is a single interval, and it means that at least one section inside that interval holds a wolf.

Write a program that counts the wolf placements satisfying all $M$ pieces of information. Two placements are different when the set of sections holding a wolf is different.

The first line contains the number of sections $N$ and the number of pieces of information $M$. ($1 \le N, M \le 300$)

Each of the next $M$ lines contains one piece of information: the left end section number $L$ and the right end section number $R$ of an interval. ($0 \le L \le R \le N-1$) The interval includes both end sections. The same interval can be given more than once.

Print the number of possible placements modulo 1,000,000,007 on the first line.