C. DFS Trees
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a connected undirected graph consisting of $n$ vertices and $m$ edges. The weight of the $i$-th edge is $i$.

Here is a wrong algorithm of finding a minimum spanning tree (MST) of a graph:

vis := an array of length ns := a set of edgesfunction dfs(u):    vis[u] := true    iterate through each edge (u, v) in the order from smallest to largest edge weight        if vis[v] = false            add edge (u, v) into the set (s)            dfs(v)function findMST(u):    reset all elements of (vis) to false    reset the edge set (s) to empty    dfs(u)    return the edge set (s)

Each of the calls findMST(1), findMST(2), ..., findMST(n) gives you a spanning tree of the graph. Determine which of these trees are minimum spanning trees.

Input

The first line of the input contains two integers $n$, $m$ ($2\le n\le 10^5$, $n-1\le m\le 2\cdot 10^5$) — the number of vertices and the number of edges in the graph.

Each of the following $m$ lines contains two integers $u_i$ and $v_i$ ($1\le u_i, v_i\le n$, $u_i\ne v_i$), describing an undirected edge $(u_i,v_i)$ in the graph. The $i$-th edge in the input has weight $i$.

It is guaranteed that the graph is connected and there is at most one edge between any pair of vertices.

Output

You need to output a binary string $s$, where $s_i=1$ if findMST(i) creates an MST, and $s_i = 0$ otherwise.

Examples
Input
5 5
1 2
3 5
1 3
3 2
4 2

Output
01111

Input
10 11
1 2
2 5
3 4
4 2
8 1
4 5
10 5
9 5
8 2
5 7
4 6

Output
0011111011

Note

Here is the graph given in the first example.

There is only one minimum spanning tree in this graph. A minimum spanning tree is $(1,2),(3,5),(1,3),(2,4)$ which has weight $1+2+3+5=11$.

Here is a part of the process of calling findMST(1):

• reset the array vis and the edge set s;
• calling dfs(1);
• vis[1] := true;
• iterate through each edge $(1,2),(1,3)$;
• add edge $(1,2)$ into the edge set s, calling dfs(2):
• vis[2] := true
• iterate through each edge $(2,1),(2,3),(2,4)$;
• because vis[1] = true, ignore the edge $(2,1)$;
• add edge $(2,3)$ into the edge set s, calling dfs(3):
• ...

In the end, it will select edges $(1,2),(2,3),(3,5),(2,4)$ with total weight $1+4+2+5=12>11$, so findMST(1) does not find a minimum spanning tree.

It can be shown that the other trees are all MSTs, so the answer is 01111.