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 $1$.

Input is given from Standard Input in the following format:

```
$N$ $M$
$s_1$ $t_1$
$s_2$ $t_2$
$\vdots$
$s_M$ $t_M$
```

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 $1$.

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

-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.