Problem Statement

We have a polynomial of degree $N, A(x)=A_Nx^N+A_{N-1}x^{N-1}+\cdots +A_1x+A_0$,
and another of degree $M, B(x)=B_Mx^M+B_{M-1}x^{M-1}+\cdots +B_1x+B_0$.
Here, each coefficient of A(x) and B(x) is an integer whose absolute value is at most 100, and the leading coefficients are not 0.
Also, let the product of them be $C(x)=A(x)B(x)=C_{N+M}x^{N+M}+C_{N+M-1}x^{N+M-1}+\cdots +C_1x+C_0$.
Given $A_0,A_1,\ldots, A_N$ and $C_0,C_1,\ldots, C_{N+M}, find B_0,B_1,\ldots, B_M$.
Here, the given inputs guarantee that there is $a unique sequence B_0, B_1, \ldots, B_M$ that satisfies the given conditions.

Input

Input is given from Standard Input in the following format:
N M
$A_0 A_1 \ldots A_{N-1} A_N$
$C_0 C_1 \ldots C_{N+M-1} C_{N+M}$

Output

Print the $M+1 integers B_0,B_1,\ldots, B_M$ in one line, with spaces in between.

Constraints

• $1 \leq N < 100$
• $1 \leq M < 100$
• $|A_i| \leq 100$
• $|C_i| \leq 10^6$
• $A_N \neq 0$
• $C_{N+M} \neq 0$
• There is $a unique sequence B_0, B_1, \ldots, B_M$ that satisfies the conditions given in the statement.

Sample Input 1

1 2
2 1
12 14 8 2

Sample Output 1

6 4 2

For A(x)=x+2 and B(x)=2x^2+4x+6, we have C(x)=A(x)B(x)=(x+2)(2x^2+4x+6)=2x^3+8x^2+14x+12, so B(x)=2x^2+4x+6 satisfies the given conditions. Thus, B_0=6, B_1=4, B_2=2 should be printed in this order, with spaces in between.

Sample Input 2

1 1
100 1
10000 0 -1

Sample Output 2

100 -1

We have A(x)=x+100, C(x)=-x^2+10000, for which B(x)=-x+100 satisfies the given conditions.
Thus, 100, -1 should be printed in this order, with spaces in between.

见题面 Input 部分

见题面 Output 部分