Safe Integer Division Check

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given integers $a,b$, check that the divisor $b$ is nonzero and the C-style integer quotient $a/b$ is greater than $2$. If $b=0$, print NO without dividing.

Input

A line contains two integers $a,b$.

Output

Print YES exactly if $b\ne0$ and the integer quotient $a/b$ exceeds $2$; otherwise NO.

Subtasks

Subtask 1 (20 points): Both integers have absolute value at most 10. Subtask 2 (30 points): Both integers have absolute value at most 10^4. Subtask 3 (50 points): Both integers have absolute value at most 10^9.

Examples

Example 1

Input

5 2

Output

NO

Explanation

C integer division gives 5 / 2 = 2, which is not greater than 2.

Example 2

Input

7 0

Output

NO

Explanation

The divisor is zero, so division is skipped and NO is printed.