Problem:
Score : 400 points

Problem Statement

There are N squares in a row.
The leftmost square contains the integer A, and the rightmost contains the integer B. The other squares are empty.

Aohashi would like to fill the empty squares with integers so that the following condition is satisfied:

For any two adjacent squares, the (absolute) difference of the two integers in those squares is between C and D (inclusive).

As long as the condition is satisfied, it is allowed to use arbitrarily large or small integers to fill the squares.
Determine whether it is possible to fill the squares under the condition.

Constraints

3 \leq N \leq 500000

0 \leq A \leq 10^9

0 \leq B \leq 10^9

0 \leq C \leq D \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B C D

Output

Print YES if it is possible to fill the squares under the condition; print NO otherwise.

Sample Input 1

5 1 5 2 4

Sample Output 1

YES

For example, fill the squares with the following integers: 1, -1, 3, 7, 5, from left to right.

Sample Input 2

4 7 6 4 5

Sample Output 2

NO

Sample Input 3

48792 105960835 681218449 90629745 90632170

Sample Output 3

NO

Sample Input 4

491995 412925347 825318103 59999126 59999339

Sample Output 4

YES

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.IOException;
import java.io.PrintWriter;
import java.util.Scanner;



/**
 * --------------------------------------------------
 * Main Class
 * --------------------------------------------------
 */
public class Main {

	public void exec() throws IOException {
		Scanner input = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int n = input.nextInt();
		int a = input.nextInt();
		int b = input.nextInt();
		int c = input.nextInt();
		int d = input.nextInt();
		
		String ret = "";
		if(d < Math.abs(b-a)/(n-1)) {
			//aとbの差が大きすぎる
			ret = "NO";
		} else if (c*2/(d-c)+2 <= n) {
			//規定回数のうちに移動不可能帯域がなくなる
			ret = "YES";
		} else {
			//nが偶数=aからbまでの遷移回数k
			int k = n-1;
			//移動可能帯域はc+dごとに繰り返しパターンを描くのでc+dの領域を調査すればOK
			int pos = Math.abs(b-a) % (c+d);
			if (k%2==1) {
				//kが奇数回
				int yesStr = c - (k-1)*(d-c)/2;
				int yesEnd = yesStr + k * (d-c);
				ret =  (yesStr <= pos && pos <= yesEnd) ? "YES" : "NO";
			} else {
				//kが偶数回
				int noStr = k*(d-c)/2;
				int noEnd = noStr + 2*c - (k+1) * (d-c);
				ret =  (noStr < pos && pos < noEnd) ? "NO" : "YES";
			}
		}
		
		out.println(ret);
		out.flush();
		input.close();
	}

	public static void main(String[] args) throws IOException {
//		long time = System.currentTimeMillis();
		new Main().exec();
//		System.out.println(System.currentTimeMillis() - time);
	}
}