/*

拆边+将每个点的边按权值排序+BFS

*/

#include<bits/stdc++.h>

#include<vector>

using namespace std;

#define N 1000005

#define ll long long

#define mod 1000000007

ll n,m;

struct Edge{ll v,w;};

//bool operator<(Edge&a,Edge&b){return a.w<b.w;}

vector<int>G[N][];

vector<int>q[N];//队列里面是一堆结点

ll ans[N],vis[N];

int main(){

    cin>>n>>m;int nn=n;

    for(int i=;i<=m;i++){

        int u,v;

        cin>>u>>v;

        int w[]={},len=,t=i;

        while(t){

            w[++len]=t%;t/=;

        }

        int l=,r=len;

        while(l<r){

            swap(w[l],w[r]);

            ++l,--r;

        }

        int pre=u;

        for(int j=;j<=len;j++){

            int newnode;

            if(j==len)newnode=v;

            else newnode=++n;

            G[pre][w[j]].push_back(newnode);

            pre=newnode;

        }

        pre=v;

        for(int j=;j<=len;j++){//反向边也要反着加

            int newnode;

            if(j==len)newnode=u;

            else newnode=++n;

            G[pre][w[j]].push_back(newnode);

            pre=newnode;

        }

    }

    int head=,tail=;

    q[++tail].push_back();vis[]=;

    for(;head<=tail;head++){

        for(int i=;i<=;i++){//先走队列头结点所有元素的0...

            int flag=;

            for(auto u:q[head]){

                for(auto v:G[u][i])if(!vis[v]){

                    vis[v]=flag=;

                    q[tail+].push_back(v);

                    ans[v]=(ans[u]*+i)%mod;

                }

            }

            if(flag)tail++;

        }

    } 

    for(int i=;i<=nn;i++)

    cout<<ans[i]<<'\n';

}