Problem 2954: 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