**Time limit:**1.00 s**Memory limit:**512 MB

**Input**

The first input line consists of two integers $n$ and $m$: the length of the signal and the length of the mask.

The next line consists of $n$ integers $a_1,a_2,\ldots,a_n$ defining the signal.

The last line consists of $m$ integers $b_1,b_2,\ldots,b_m$ defining the mask.

**Output**

Print $n+m-1$ integers: the sum of products of aligned values at each mask position from left to right.

**Constraints**

- $1 \le n,m \le 2 \cdot 10^5$

- $1 \le a_i,b_i \le 100$

**Example**

Input:

`5 3`

1 3 2 1 4

1 2 3

Output:

`3 11 13 10 16 9 4`

Explanation: For example, at the second mask position the sum of aligned products is $2 \cdot 1 + 3 \cdot 3 = 11$.