Sum of Odd Integers

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

Given positive n,k, determine whether n is the sum of exactly k pairwise distinct positive odd integers. PHOJ accepts one n,k pair; the original Codeforces version has t cases.

Input

Two positive integers n k.

Output

Print YES if possible; otherwise NO.

Subtasks

• Subtask 1 (20%): 1 ≤ n,k ≤ 100.

• Subtask 2 (30%): 1 ≤ n,k ≤ 10^5.

• Subtask 3 (50%): 1 ≤ n,k ≤ 10^7.

Examples

Example 1

Input:

10 2

Output:

YES

Explanation: 10=3+7 uses two distinct odd positive integers.

Example 2

Input:

10 3

Output:

NO

Explanation: Three odd integers have odd sum, not ten.

Example 3

Input:

16 4

Output:

YES

Explanation: The smallest four distinct positive odd integers sum to 16.