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

**Input**

The first input line has two integers $n$ and $m$: the number of levels and teleporters. The levels are numbered $1,2,\dots,n$.

After this, there are $m$ lines describing the teleporters. Each line has two integers $a$ and $b$: there is a teleporter from level $a$ to level $b$.

**Output**

Print one integer: the number of ways you can complete the game. Since the result may be large, print it modulo $10^9+7$.

**Constraints**

- $1 \le n \le 10^5$

- $1 \le m \le 2 \cdot 10^5$

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

**Example**

Input:

`4 5`

1 2

2 4

1 3

3 4

1 4

Output:

`3`