Binomial Coefficients

Time Limit: 1000MS

Memory Limit: 131072K

Description

The binomial coefficient C(n, k) has been extensively studied for its importance in combinatorics. Binomial coefficients can be recursively defined as follows:
C(n, 0) = C(n, n) = 1 for all n > 0; C(n, k) = C(n − 1, k − 1) + C(n − 1, k) for all 0 < k < n.
Given n and k, you are to determine the parity of C(n, k).

Input

The input contains multiple test cases. Each test case consists of a pair of integers n and k (0 ≤ kn < 231, n > 0) on a separate line.End of file (EOF) indicates the end of input.

Output

For each test case, output one line containing either a “0” or a “1”, which is the remainder of C(n, k) divided by two.

Sample Input

1 1
1 0
2 1

Sample Output

1
1
0

Hint

Source

PKU Local 2007 (POJ Monthly--2007.04.28), Ikk

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