martin

Martin.

Martin chooses two natural numbers $a$ and $b$. He also chooses a number $k$ and calculates the numbers $x$ and $y$, which represent the remainders of $a$ and $b$, respectively, when divided by $k$.

Task

Given the numbers $k$, $x$, $y$, and the sum $s = a+b$, determine if we can choose two numbers $a$ and $b$ that meet Martin's conditions.

Input data

The first line contains 4 numbers $k$, $x$, $y$, and $s$ as described in the statement.

Output data

If two numbers can be chosen to meet the conditions, print DA (yes in Romanian), otherwise print NU (no in Romanian).

Constraints and clarifications

• $1 \leq k \leq 1\ 000\ 000\ 000$;
• $0 \leq x, y < k$;
• $1 \leq s \leq 2\ 000\ 000\ 000$;

Example 1

stdin

5 2 4 11

stdout

DA

Explanation

The solution $a=7$ and $b=4$ meets the conditions.

Example 2

stdin

7 2 5 9

stdout

NU