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

Query number i is given as a pair of integers l_i, r_i (1 ≤ l_i ≤ r_i ≤ n).
The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum a_{l_i} + a_{l_i + 1} + ... + a_{r_i} = 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, ..., a_n (a_i = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers l_i, r_i (1 ≤ l_i ≤ r_i ≤ n).

Output

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

Eugeny and Array

Examples