Sign of Integer Division

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given integers $a,b$, first reject a zero divisor. Otherwise compute the C integer quotient (truncate towards zero), then classify its sign.

Input

One line with two integers $a,b$.

Output

Print INVALID if $b=0$. Otherwise print POS, ZERO, or NEG according to the sign of the integer quotient $a/b$.

Subtasks

• Subtask 1 (20 points): $-10\le a,b\le 10$. $b\ne0$.
• Subtask 2 (30 points): $-100\le a,b\le 100$.
• Subtask 3 (50 points): $-1000\le a,b\le 1000$.

Examples

Example 1

Input

-7 2

Output

NEG

Explanation

The input gives -7, 2. The divisor is 2; C-style integer division -7/2 truncates towards zero, yielding -3. Therefore the required output is ['NEG'].

Example 2

Input

1 2

Output

ZERO

Explanation

The input gives 1, 2. The divisor is 2; C-style integer division 1/2 truncates towards zero, yielding 0. Therefore the required output is ['ZERO'].

Example 3

Input

5 0

Output

INVALID

Explanation

The input gives 5, 0. The divisor is 0; division is invalid. Therefore the required output is ['INVALID'].