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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include<vector>
#include<queue>
#include<map>
#include<algorithm>
#include<cstring>
#include<string>
#include <set>
#include <cassert>
#include<cmath>
#include<climits>
#include<iomanip>
using namespace std;
#define MOD 1000000007
#define REP(i,n) for(int (i)=0;(i)<(n);(i)++)
#define FOR(i,c) for(decltype((c).begin())i=(c).begin();i!=(c).end();++i)
#define ll long long
#define all(hoge) (hoge).begin(),(hoge).end()
const long long INF = 1LL << 60;
typedef vector<ll> Array;
typedef vector<Array> Matrix;



struct Edge {//グラフ
	ll to, cap, rev;
	Edge(ll _to, ll _cap, ll _rev) {
		to = _to; cap = _cap; rev = _rev;
	}
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &G, ll from, ll to, ll cap) {//最大フロー求める Ford-fulkerson
	G[from].push_back(Edge(to, cap, (ll)G[to].size()));
	G[to].push_back(Edge(from, 0, (ll)G[from].size() - 1));
}
ll max_flow_dfs(Graph &G, ll v, ll t, ll f,vector<bool> &used)
{
	if (v == t)
		return f;
	used[v] = true;
	for (int i = 0; i < G[v].size(); ++i) {
		Edge &e = G[v][i];
		if (!used[e.to] && e.cap > 0) {
			ll d = max_flow_dfs(G,e.to, t, min(f, e.cap),used);
			if (d > 0) {
				e.cap -= d;
				G[e.to][e.rev].cap += d;
				return d;
			}
		}
	}
	return 0;
}
ll max_flow(Graph &G, ll s, ll t)
{
	ll flow = 0;
	for (;;) {
		vector<bool> used(G.size());
		REP(i, used.size())used[i] = false;
		ll f = max_flow_dfs(G,s, t, INF,used);
		if (f == 0) {
			return flow;
		}
		flow += f;
	}
}

template<class T> inline bool chmin(T& a, T b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}
template<class T> inline bool chmax(T& a, T b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}

class UnionFind {
	vector<int> data;
public:
	UnionFind(int size) : data(size, -1) { }
	bool unionSet(int x, int y) {
		x = root(x); y = root(y);
		if (x != y) {
			if (data[y] < data[x]) swap(x, y);
			data[x] += data[y]; data[y] = x;
		}
		return x != y;
	}
	bool findSet(int x, int y) {
		return root(x) == root(y);
	}
	int root(int x) {
		return data[x] < 0 ? x : data[x] = root(data[x]);
	}
	int size(int x) {
		return -data[root(x)];
	}
};


//約数求める //約数
void divisor(ll n,vector<ll> &ret) {
	for (ll i = 1; i * i <= n; i++) {
		if (n % i == 0) {
			ret.push_back(i);
			if (i * i != n) ret.push_back(n / i);
		}
	}
	sort(ret.begin(), ret.end());
	
}
//階乗
long long factorial(long long n, long long mod) {
	long long ret = 1;
	for (long long i = 1; i <= n; i++) {
		ret = (ret * i) % mod;
	}
	return ret;
}
//モジュラ逆数
long long inv_mod(long long n, long long mod) {
	long long a = n % mod, b = mod - 2, ret = 1;
	while (b > 0) {
		if (b & 1) ret = (ret * a) % mod;
		a = (a * a) % mod;
		b >>= 1;
	}
	return ret;
}

long long nPr(long long n, long long r, long long mod) {
	long long ret = 1;
	for (long long i = n; i >= n - r + 1; i--) {
		ret = ret * (i % mod) % mod;
	}
	return ret;
}

long long nCr(long long n, long long r, long long mod) {
	return nPr(n, r, mod) * inv_mod(factorial(r, mod), mod) % mod;
}

bool compare_by_b(pair<ll, ll> a, pair<ll, ll> b) {//降順second
	if (a.second != b.second) {
		return a.second > b.second;
	}
	else {
		return a.first > b.first;
	}
}

bool compare_by_a(pair<ll, ll> a, pair<ll, ll> b) {//降順first
	if (a.first != b.first) {
		return a.first > b.first;
	}
	else {
		return a.second > b.second;
	}
}

ll gcd(ll m, ll n){
	if (n == 0)return m;
	return gcd(n, m%n);
}//gcd


int main() {
	ll n, a, b, c, d;
	cin >> n >> a >> b >> c >> d;
	ll dif = abs(a - b);
	ll min = (n - 1)*c;
	ll max = (n - 1)*d;
	while (1) {
		if (min <= dif && dif <= max) {
			cout << "YES";
			return 0;
		}
		min -= (c+d) ;
		max -= (c+d);
		if (max < 0)break;
	}
	cout << "NO";
	return 0;
}