Coin Piles

Source: CSES

Version: Phuoc Hung OJ Extended

Problem Statement

Two piles contain $a$ and $b$ coins. Each operation removes one coin from one pile and two from the other, in either orientation. Determine if both piles can be emptied.

Input

One line contains integers $a,b$, the initial pile sizes.

Output

Print YES if both piles can be emptied, otherwise NO.

Subtasks

• Subtask 1 (20 points): 0 <= a,b <= 10.

• Subtask 2 (30 points): 0 <= a,b <= 100000.

• Subtask 3 (50 points): 0 <= a,b <= 1e9.

Examples

Example 1

Input

2 1

Output

YES

Explanation

For this input, the case-specific computation and the required exact output are shown above. One operation of type (2,1) empties the piles.

Example 2

Input

2 2

Output

NO

Explanation

For this input, the case-specific computation and the required exact output are shown above. Four coins cannot be removed in steps of exactly three coins.