System of Linear Equations

You are given n\cdot(m+1) coefficients a_{i,j} and b_i which form the following n linear equations:

a_{1,1}x_1 + a_{1,2}x_2 + \dots + a_{1,m}x_m = b_1 \pmod {10^9 + 7}

a_{2,1}x_1 + a_{2,2}x_2 + \dots + a_{2,m}x_m = b_2 \pmod {10^9 + 7}

\dots

a_{n,1}x_1 + a_{n,2}x_2 + \dots + a_{n,m}x_m = b_n \pmod {10^9 + 7}

Your task is to find any m integers x_1, x_2, \dots, x_m that satisfy the given equations.

Input

The first line has two integers n and m: the number of equations and variables. The next n lines each have m+1 integers a_{i,1}, a_{i,2}, \dots, a_{i,m}, b_i: the coefficients of the i-th equation.

Output

Print m integers x_1, x_2,\dots, x_m: the values of the variables that satisfy the equations. The values must also satisfy 0 \le x_i < 10^9 + 7. You can print any valid solution. If no solution exists print only -1.

Constraints

$1 \le n, m \le 500$

0 \le a_{i,j}, b_i &lt; 10^9 + 7

Example

Input

3 3
2 0 1 7
1 2 0 0
1 3 1 2

Output

2 1000000006 3