### Multiplication

Time Limit: 2000/1000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

#### Problem Description

If $$C = A \diamond B$$, then $C[k] = \sum_{\max(i, j) = k} A[i] \cdot B[j] \bmod (10^9 + 7)$.

Work out sequence $$C = A \diamond B$$ for given sequence $$A$$ and $$B$$.

#### Input

The first line contains a integer $$n$$, which denotes the length of sequence $$A, B$$.

The second line contains $$n$$ integers $$a_1, a_2, \ldots, a_n$$, which denote sequence $$A$$.

The thrid line contains $$n$$ integers $$b_1, b_2, \ldots, b_n$$, which denote sequence$$B$$.

($$1 \leq n \leq 10^5, 0 \leq a_i, b_i \leq 10^9$$)

#### Output

$$n$$ integers, which denotes sequence $$C$$.

#### Sample Input

2
1 2
3 4


#### Sample Output

3 18

ftiasch

#### Manager

Information
 Solved Number 114 Submit Number 364
Problem Tags
implementation
math
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