Eugeny and Array

Eugeny has array a = a1, a2, ..., an, consisting of n integers. Each integer ai equals to -1, or to 1. Also, he has m queries:

• Query number i is given as a pair of integers li, ri (1 ≤ li ≤ ri ≤ n).
• The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum ali + ali + 1 + ... + ari = 0, otherwise the response to the query will be integer 0.

Help Eugeny, answer all his queries.

Input

The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).

Output

Print m integers — the responses to Eugene's queries in the order they occur in the input.

Examples

Input

2 3 1 -1 1 1 1 2 2 2

Output

0 1 0

Input

5 5 -1 1 1 1 -1 1 1 2 3 3 5 2 5 1 5

Output

0 1 0 1 0

inputFormat

Input

The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).

outputFormat

Output

Print m integers — the responses to Eugene's queries in the order they occur in the input.

Examples

Input

2 3 1 -1 1 1 1 2 2 2

Output

0 1 0

Input

5 5 -1 1 1 1 -1 1 1 2 3 3 5 2 5 1 5

Output

0 1 0 1 0

样例

5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5

0
1
0
1
0

</p>