Problem Description
In a directed graph which has N points and M edges,points are labled from 1 to n.At first I am at point u,at each step I will choose an output edge of the current point at uniform random,for every point Z,please output the possibility of reaching the point Z,moving exactly K steps.
Input
the first line contains two positive intergesN,M,means the number of points and edges.
next M lines,contains two positive intergersX,Y,means an directed edge from X to Y.
next line there is an integer Q,means the number of queries.
next Q lines,each line contains two integers u,K,means the first point and number of the steps.
N≤50,M≤1000,Q≤20,u≤N,K≤109.
Every point have at least one output edge.
Output
Q lines,each line contains N numbers,the i-th number means the possibility of reaching point i from u,moving exactly K steps.
In consideration of the precision error,we make some analyses,finding the answer can be represented as the form like XY,you only need to output X×Y109+5 mod (109+7).
You need to output an extra space at the end of the line,or you will get PE.
Sample Input
3 2
1 2
1 3
1
1 1
Sample Output
0 500000004 500000004
I am now at point $1$,by one move,with a possibity of $\frac{1}{2}$ of reaching point 2,with a possibity of $\frac{1}{2}$ of reaching point 3,so we need to output 0 0.5 0.5,but as what is said above,we need to output$1*2^{10^9+5}~mod~{10^9+7}=500000004$.
