Migrated from Lutece 1048 Bob's vector

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Description

Bob has a vector with $m$ elements, called vector $B$. Now Alice gives him a vector $X$ with $n$ elements.

Then he gets a new vector $A$, in which $A_i = (B_1 \times X_i+ B_2 \times X_i ^ 2 \cdots +B_{m-1} \times X_i ^{m-1}+B_m \times X_i^m)$ mod $1000000007$.

Now Alice wants to find a peak position in vector $A$, and a peak position is a position whose value is greater than both of its neighbors. You may assume that $A_0 = - \infty, A_{n + 1}=-\infty$.

As is known to everyone of you, Bob loves Alice very much. Could you tell Bob the answer to help Bob leave a good impression on Alice.

Input

The frist line contains $2$ integers $n, m$, indicating the size of vector $X$ and the size of vector $B$.

The second line contains $n$ integers $X_i(0 \leq X_i \leq 1000000000)$, indicating the element in the vector $X$.

The last line contains $m$ integers $B_i(0 \leq B_i \leq 1000000000)$, indicating the element in the vector $B$.

It is guaranteed that $1 \leq n \leq 500000, 1 \leq m \leq 10000$, and $A_i \neq A_{i + 1}(1 \leq i < n)$ .

Output

Print a single integer, which denotes a peak position. If there are multiple solutions, you may print any of them.

Samples

3 2
2 1 3
1 1

1

Note

$A_0=-\infty, A_1=6, A_2=2, A_3=12, A_4=-\infty$. So $1$, $3$ are both OK

Resources

The 13th UESTC Programming Contest Final