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: Wrong Answer)

import java.io.*;
import java.lang.reflect.Array;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;


  public class Main {
	private InputStream is;
	private PrintWriter out;
	int time = 0, dp[][], DP[][], prime[], start[], parent[], end[], val[], black[], arr[], arr1[][];
	long  MOD = (long)(1e9+7);
	ArrayList<Integer>[] amp;
	boolean b[], b1[];
	Pair prr[];
	char ch[][],c[];
	HashSet<Integer> hs1 = new HashSet<>(), hs2 = new HashSet<>();

	public static void main(String[] args) throws Exception {
		new Thread(null, new Runnable() {
		public void run() {
			try {

		//new Main().soln();
		} catch (Exception e) {
				System.out.println(e);
			}
		}
	}, "1", 1 << 26).start();
		new Main().soln();
	}
	int MAX = 1000010, N, K, p = 1;
	PriorityQueue<Pair> pq;
	int Dp[][] = new int[1010][1010];
	void solve() {
		int n = ni();
		long a = nl(), b = nl(), c = nl(), d = nl();
		long diff = Math.abs(b-a);
			if(n%2==0 && diff>=c && diff<=d){
				System.out.println("YES");
				return;
			}
			for(int i = 0;i<(n-1);i++){
				long sum = c*i - d*(n-2-i) + a;
				if((sum<=(b+d) && sum>=(b+c)) || (sum>=(b-d) && sum<=(b-c))){
					System.out.println("YES");
					return;
				}
			}
			for(int i = 0;i<(n-1);i++){
				long sum = -c*i + d*(n-2-i) + a;
				if((sum<=(b+d) && sum>=(b+c)) || (sum>=(b-d) && sum<=(b-c))){
					System.out.println("YES");
					return;
				}
			}
			for(int i = 0;i<(n-1);i++){
				long sum = c*i + d*(n-2-i) + a;
				if((sum<=(b+d) && sum>=(b+c)) || (sum>=(b-d) && sum<=(b-c))){
					System.out.println("YES");
					return;
				}
			}
			for(int i = 0;i<(n-1);i++){
				long sum = -c*i - d*(n-2-i) + a;
				if((sum<=(b+d) && sum>=(b+c)) || (sum>=(b-d) && sum<=(b-c))){
					System.out.println("YES");
					return;
				}
			}
			System.out.println("NO");
	}
	class Node{
		Node left, right;
		int data;
		Node(int x){
			data = x;
		}
	}
	class BST{
		Node root;
		Node pre;
		void insert(int x){
			if(root==null){
				root = new Node(x);
				return;
			}
			Node temp = root;
			Node prev = temp;
			while(temp!=null){
				int y = temp.data;
				prev = temp;
				if(y>x) temp = temp.left;
				if(y<x) temp = temp.right;
			}
			if(prev.data>x) prev.left = new Node(x);
			else prev.right = new Node(x);
		}
		Node search(int x){
			Node temp = root;
			pre = null;
			while(temp!=null){
				int y = temp.data;
				if(y==x) return temp;
				pre = temp;
				if(y>x) temp = temp.left;
				if(y<x) temp = temp.right;
			}
			return null;
		}
		void delete(int x){
			Node n = search(x);
			if(n==null){
				System.out.println("No such element");
			}
			else if(n.left==null && n.right==null){
				if(pre!=null){
					if(pre.data>x) pre.left = null;
					else pre.right = null;
				}
				else root = null;
			}
			else if(n.left==null){
				while(n.right!=null){
					
				}
			}
			else if(n.right==null){
				
			}
			else{
				
			}
		}
		void inOrder(Node n){
			if(n==null) return;
			inOrder(n.left);
			System.out.print(n.data+"->");
			inOrder(n.right);
		}
	}
	void dfs(int x){
		//System.out.println(x+" "+hs1);
		boolean[] b = new boolean[arr1[x].length];
		for(int i = 0; i<arr1[x].length;i++){
			int val = arr1[x][i];
			if(val>0 && !hs1.contains(val)){
				hs1.add(val);
				b[i] = true;
			}
			else if(hs1.contains(val*-1)){
				hs1.remove(val*-1);
				b[i] = true;
			}
		}
		//System.out.println(x+" * "+hs1);
		end[x] = hs1.size();
		for(int i : amp[x])
			dfs(i);
		for(int i = 0; i<arr1[x].length; i++){
			if(b[i]){
				int val = arr1[x][i];
				if(val>0){
					if(hs1.contains(val)) hs1.remove(val);
				}
				else hs1.add(val*-1);
			}
		}
		//System.out.println(hs1+" "+x);
	}
	long[] mul(long arr[][], long temp[]){
		long ans[] = new long[temp.length];
		for(int i = 0; i<arr.length;i++){
			long sum = 0;
			for(int j = 0; j<arr.length;j++){
				sum = (sum+arr[i][j]*temp[j])%MOD;
			}
			ans[i] = sum;
		}
		return ans;
	}
	void printMat(long arr[][]){
		for(int i = 0; i< arr.length; i++){
			for(int j = 0; j < arr.length ;j++){
				System.out.print(arr[i][j]+" ");
			}
			System.out.println();
		}
		System.out.println("-----");
	}
	void printMat(long arr[]){
		for(int i = 0; i< arr.length; i++){
				System.out.print(arr[i]+" ");
		}
		System.out.println();
		System.out.println("-----");
	}
	long[][] matMul(int n, long arr[][], long y){
		long iden[][] = new long[n][n];
		for(int i= 0; i< n; i++) iden[i][i] = 1;
		//printMat(iden);
		while(y>0){
			if(y%2==1){
				iden = mul(n,iden,arr);
				//printMat(iden);
				y--;
			}
			else{
				arr = mul(n,arr,arr);
				//printMat(arr);
				y/=2;
			}
		}
		return iden;
	}
	long[][] mul(int n , long a1[][], long a2[][]){
		long temp[][] = new long[n][n];
		for(int i = 0; i< n; i++){
			for(int j = 0; j<n; j++){
				long sum = 0;
				for(int k = 0; k<n;k++){
					sum = (sum+a1[i][k]*a2[k][j])%MOD;
				}
				temp[i][j] = sum;
			}
		}
		return temp;
	}
	void seive(int n){
		b = new boolean[n+1];
		prime = new int[n+1];
		for(int i = 2;i*i<=n;i++){
			if(!b[i]){
				for(int j = 2*i; j<=n;j+=i){
					if(!b[j]){
						b[j] = true;
						prime[j] = i;
					}
				}
			}
		}
	}
	int binarySearch1(int arr[], int x){
		int ans = -1;
		int low = 0, high = arr.length-1;
		while(high>=low){
			int mid = (low+high)/2;
			if(arr[mid]>=x){
				ans = mid;
				high = mid-1;
			}
			else low = mid+1;
		}
		return ans;
	}
	int binarySearch2(Integer arr[], int x){
		int ans = -1;
		int low = 0, high = arr.length-1;
		while(high>=low){
			int mid = (low+high)/2;
			if(arr[mid]>=x){
				ans = mid;
				low = mid+1;
			}
			else high = mid-1;
		}
		return ans+1;
	}
	int cntEven(String str){
		int cnt = 0;
		for(int i = str.length()-1; i >= 0; i--){
			if((str.charAt(i)-'0')%2==0){
				cnt++;
			}
		}
		return cnt;
	}
	int max = 0;
	int getParent(int x){
		//System.out.println(x+" "+parent[x]);
		if(parent[x]!=x){
			parent[x] = getParent(parent[x]);
		}
		return parent[x];
	}
	class Pair implements Comparable<Pair>{
		int u;
		int v, r;
		Pair(int u, int v, int r){
			this.u = u;
			this.v = v;
			this.r = r;
		}
		Pair(int u, int v){
			this.u = u;
			this.v = v;
		}public int hashCode() {
			return Objects.hash();
		}
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return ((u == other.u && v == other.v));// || (v == other.u && u == other.v));
		}
		public int compareTo(Pair other) {
			return Long.compare(u, other.u);
			//return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v, other.v) != 0 ? (Long.compare(v, other.v)) :(Long.compare(other.r, r))) ;
		}	
		public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}
	}
	int min(int x,int y){
		if(x<y) return x;
		return y;
	}
	int max(int x,int y){
		if(x>y) return x;
		return y;
	}
	void buildGraph(int m){
		while(m-->0)
		{
			int x = ni()-1, y = ni()-1;
			amp[x].add(y);
			amp[y].add(x);
		}
	}
	long modInverse(long a, long mOD2){
        return  power(a, mOD2-2, mOD2);
	}
	long power(long x, long y, long m)
	{
		if (y == 0)
    return 1;
	long p = power(x, y/2, m) % m;
	p = (p * p) % m;

	return (y%2 == 0)? p : (x * p) % m;
	}
	boolean isPrime(int x){
		for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
		return true;
	}
	public long gcd(long a, long b){
		if(b==0) return a;
		return gcd(b,a%b);
	}
	void failFn(String str, int arr[]){
		int len = 0;
		arr[0] = 0;
		int i = 1;
		while(i<arr.length){
			if(str.charAt(i)==str.charAt(len)){
				arr[i++] = ++len;
				continue;
			}
			if(len == 0){
				arr[i] = len;
				i++;
				continue;
			}
			if(str.charAt(i)!=str.charAt(len)){
				len = arr[len-1];
			}
		}
	}
	static class ST1{
		int arr[], st[], size;
		ST1(int a[]){
			arr = a.clone();
			size = 10*arr.length;
			st = new int[size];
			build(0,arr.length-1,1);
		}
		void build(int ss, int se, int si){
			if(ss==se){
				st[si] = arr[ss];
				return;
			}
			int mid = (ss+se)/2;
			int val = 2*si;
			build(ss,mid,val); build(mid+1,se,val+1);
			st[si] = (st[val]+ st[val+1]);
		}
		int get(int ss, int se, int l, int r, int si){
			if(l>se || r<ss || l>r) return Integer.MAX_VALUE;
			if(l<=ss && r>=se) return st[si];
			int mid = (ss+se)/2;
			int val = 2*si;
			return (get(ss,mid,l,r,val)+ get(mid+1,se,l,r,val+1));
		}
	}
	static class ST{
		int arr[],lazy[],n;
		ST(int a){
			n = a;
			arr = new int[10*n];
			lazy = new int[10*n];
		}
		void up(int l,int r,int val){
			update(0,n-1,0,l,r,val);
		}
		void update(int l,int r,int c,int x,int y,int val){
			if(lazy[c]!=0){
				lazy[2*c+1]+=lazy[c];
				lazy[2*c+2]+=lazy[c];
				if(l==r)
					arr[c]+=lazy[c];
				lazy[c] = 0;
			}
			if(l>r||x>y||l>y||x>r)
				return;
			if(x<=l&&y>=r){
				lazy[c]+=val;
				return ;
			}
			int mid = l+r>>1;
			update(l,mid,2*c+1,x,y,val);
			update(mid+1,r,2*c+2,x,y,val);
			arr[c] = (arr[2*c+1]+ arr[2*c+2]);
		}
		int an(int ind){
			return ans(0,n-1,0,ind);
		}
		int ans(int l,int r,int c,int ind){
			if(lazy[c]!=0){
				lazy[2*c+1]+=lazy[c];
				lazy[2*c+2]+=lazy[c];
				if(l==r)
					arr[c]+=lazy[c];
				lazy[c] = 0;
			}
			if(l==r)
				return arr[c];
			int mid = l+r>>1;
			if(mid>=ind)
				return ans(l,mid,2*c+1,ind);
			return ans(mid+1,r,2*c+2,ind);
		}
	}
	public static class FenwickTree {
		
	    long[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates

	    public FenwickTree(int size) {
	        array = new long[size + 1];
	    }
	    public long rsq(int ind) {
	        assert ind > 0;
	        long sum = 0;
	        while (ind > 0) {
	            sum += array[ind];
	            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
	            ind -= ind & (-ind);
	        }
	        return sum;
	    }
	    public long rsq(int a, int b) {
	        assert b >= a && a > 0 && b > 0;
	        return rsq(b) - rsq(a - 1);
	    }
	    public void update(int ind, long value) {
	        assert ind > 0;
	        while (ind < array.length) {
	            array[ind] += value;
	            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
	            ind += ind & (-ind);
	        }
	    }
	    public int size() {
	        return array.length - 1;
	    }
	}
	public static int[] shuffle(int[] a, Random gen){
		for(int i = 0, n = a.length;i < n;i++)
		{ 
			int ind = gen.nextInt(n-i)+i; 
			int d = a[i]; 
			a[i] = a[ind];
			a[ind] = d; 
		} 
	return a; 
	}
	long power(long x, long y, int mod){
		long ans = 1;
		while(y>0){
			if(y%2==0){
				x = (x*x)%mod;
				y/=2;
			}
			else{
				ans = (x*ans)%mod;
				y--;
			}
		}
		return ans;
	}
	void soln() {
		is = System.in;
		out = new PrintWriter(System.out);
		long s = System.currentTimeMillis();
		solve();
		out.close();
		out.flush();
		tr(System.currentTimeMillis() - s + "ms");
	}


	// To Get Input
	// Some Buffer Methods
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}
	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
									// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}