F - Blocked Roads

Score : $500$ points

Problem Statement

You are given a directed graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ $(1 \leq i \leq M)$ goes from Vertex $s_i$ to Vertex $t_i$ and has a length of $1$.

For each $i$ $(1 \leq i \leq M)$, find the shortest distance from Vertex $1$ to Vertex $N$ when all edges except Edge $i$ are passable, or print -1 if Vertex $N$ is unreachable from Vertex $1$.

Constraints

• $2 \leq N \leq 400$
• $1 \leq M \leq N(N-1)$
• $1 \leq s_i,t_i \leq N$
• $s_i \neq t_i$
• $(s_i,t_i) \neq (s_j,t_j)$ $(i \neq j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$s_1$ $t_1$

$s_2$ $t_2$

$\vdots$

$s_M$ $t_M$

Output

Print $M$ lines.

The $i$-th line should contain the shortest distance from Vertex $1$ to Vertex $N$ when all edges except Edge $i$ are passable, or -1 if Vertex $N$ is unreachable from Vertex $1$.

3 3
1 2
1 3
2 3

1
2
1

4 4
1 2
2 3
2 4
3 4

-1
2
3
2

Vertex $N$ is unreachable from Vertex $1$ when all edges except Edge $1$ are passable, so the corresponding line contains -1.

5 10
1 2
1 4
1 5
2 1
2 3
3 1
3 2
3 5
4 2
4 3

1
1
3
1
1
1
1
1
1
1

4 1
1 2

-1