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

• $a_{1,1}x1 + a{1,2}x2 + \dots + a{1,m}x_m = b_1 \pmod {10^9 + 7}$
• $a_{2,1}x1 + a{2,2}x2 + \dots + a{2,m}x_m = b_2 \pmod {10^9 + 7}$
• $\dots$
• $a_{n,1}x1 + a{n,2}x2 + \dots + a{n,m}x_m = b_n \pmod {10^9 + 7}$

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

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.

• $1 \le n, m \le 500$
• $0 \le a_{i,j}, b_i < 10^9 + 7$

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 $-1$ .