A. Eugeny and Array
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Eugeny has array a = a 1, a 2, ..., 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 a 1, a 2, ..., 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.

Examples
Input
2 31 -11 11 22 2
Output
010
Input
5 5-1 1 1 1 -11 12 33 52 51 5
Output
01010