## CR07C3P5 - BICIKLI

A bicycle race is being organized in a land far, far away. There are N town in the land, numbered 1 through N. There are also M one-way roads between the towns. The race will start in town 1 and end in town 2. How many different ways can the route be set? Two routes are considered different if they do not use the exact same roads.

### Input

The first line of input contains two integers N and M (1 ≤ N ≤ 10 000, 1 ≤ M ≤ 100 000), the number

of towns and roads.

Each of the next M lines contains two different integers A and B, representing a road between towns A

and B.

Towns may be connected by more than one road.

### Output

Output the number of distinct routes that can be set on a single line. If that number has more than nine

digits, output only the last nine digits of the number. If there are infinitely many routes, output "inf".

### Example

Input:6 7 1 3 1 4 3 2 4 2 5 6 6 5 3 4Output:3

Input:6 8 1 3 1 4 3 2 4 2 5 6 6 5 3 4 4 3Output:inf

Input:31 60 1 3 1 3 3 4 3 4 4 5 4 5 5 6 5 6 6 7 6 7 … … … 28 29 28 29 29 30 29 30 30 31 30 31 31 2 31 2Output:073741824

Added by: | Ahmed Salem [mrtempo] |

Date: | 2015-01-17 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 JS-MONKEY |

Resource: | COCI 2006/2007 #3 (http://hsin.hr/coci/archive/2006_2007/contest3_tasks.pdf) |