**Time limit:**1.00 s**Memory limit:**512 MB

**Input**

The first input line has two integers $n$ and $m$: the number of cities and flights. The cities are numbered $1,2,\dots,n$. City $1$ is Syrjälä, and city $n$ is Lehmälä.

Then, there are $m$ lines describing the flights. Each line has two integers $a$ and $b$: there is a flight from city $a$ to city $b$. All flights are one-way flights.

**Output**

Print one integer: the number of routes modulo $10^9+7$.

**Constraints**

- $2 \le n \le 20$

- $1 \le m \le n^2$

- $1 \le a,b \le n$

**Example**

Input:

`4 6`

1 2

1 3

2 3

3 2

2 4

3 4

Output:

`2`