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

Example Output

3