You are given two integers N and K.

Calculate the value of the following mathematical expression:

N ⊕ (N + 1) ⊕ (N + 2) ⊕ ... ⊕ K

where ⊕ represents the bitwise XOR operation.

Since N and K can be very large, an efficient solution is required.

Input Format

The first line contains two integers:

N K

Output Format

Print the XOR of all integers from N to K, inclusive.

Constraints

1 ≤ N ≤ K ≤ 10^18

Example

Input: 3 7

Output: 3

Explanation:

3 ⊕ 4 ⊕ 5 ⊕ 6 ⊕ 7 = 3