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

A game has n levels, connected by m teleporters, and your task is to get from level 1 to level n. The game has been designed so that there are no directed cycles in the underlying graph. In how many ways can you complete the game?

# 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