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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i, n) for(int i=0; i<(n); ++i)
#define rep2(i, s, n) for(int i=s; i<(n); ++i)
#define ALL(v) (v).begin(), (v).end()

using namespace std;

typedef long long ll;

template<typename T>
using priority_queue_rev = priority_queue<T, vector<T>, greater<T> >;

static const int INTINF = (2147483647 >> 1); // 10^9 + 5000
static const ll LLINF = (9223372036854775807 >> 1);
static const int MAX = 1e5+1;
static const ll MOD = 1e9+7;

namespace Kunitaka{
    template<
        typename TYPE,
        std::size_t SIZE
    >
    std::size_t array_length(const TYPE (&array)[SIZE])
    {
        return SIZE;
    }

    template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
    template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
}
using namespace Kunitaka;
namespace Printer{
    void br(){
        cout << endl;
    }

    void loop_cnt(int i){
        cout << "i = " << i << endl;
    }

    void loop_cnt(int i, int j){
        cout << "i = " << i << ", " << "j = " << j << endl;
    }

    template<class T>
    void print(T x){
        cout << x << endl;
    }

    template<class T, class S>
    void print(T x, S y){
        cout << x << "," << y << endl;
    }

    template<class T, class S, class U>
    void print(T x, S y, U z){
        cout << x << "," << y << "," << z << endl;
    }

    template<class T, class S>
    void print(pair<T, S> p){
        cout << p.first << ", " << p.second << endl;
    }

    template<
        typename TYPE,
        std::size_t SIZE
    >
    void print(const TYPE (&array)[SIZE]){
        int lim = array_length(array);
        for(int i=0; i<lim; i++){
            if(i) cout << " ";
            cout << array[i];
        }
        cout << endl;
    }

    template<class S>
    void print(vector<S> v){
        for(int i=0; i<v.size(); i++){
            if(i) cout << " ";
            cout<< v[i];
        }
        cout << endl;
    }

    template<class S>
    void print(vector<vector<S> > vv){
        for(int i=0; i<vv.size(); i++){
            for(int j=0; j<vv[i].size(); j++){
                if(j) cout << " ";
                cout << vv[i][j];
            }
            cout << endl;
        }
    }

    void yesno(bool x){
        if(x) cout << "Yes" << endl;
        else cout << "No" << endl;
    }
};
using namespace Printer;

int main(int argc, const char * argv[]) {
    //提出時、消す----//


    // input
    cout << fixed << setprecision(10);
    ll N; cin >> N;
    ll num = N - 1;
    ll A, B; cin >> A >> B;
    B -= A;
    ll C, D; cin >> C >> D;
    ll sum = 0;
    rep(i, num){
        sum += -D;
    }

    bool ans = false;
    rep(i, num){
        // cout << sum << endl;
        if(B < sum){
            ans = false;
            break;
        } else{
            ll num1 = - C + D;
            ll num2 = num1 + C * 2;
            ll num3 = num2 + D - C;
            if(sum <= B && B <= sum + num1){
                // print(1);
                ans = true;
                break;
            } else if(sum + num1 < B && B < sum + num2){
                sum += num1;
            } else if(sum + num2 <= B && B <= sum + num3){
                // print(2, sum + num2, sum + num3);
                // print(B);
                ans = true;
                break;
            } else{
                sum += num3;
            }
        }
    }
    // cout << sum << endl;
    
    if(ans){
        cout << "YES" << endl;
    }
    else{
        cout << "NO" << endl;
    }
    
    return 0;
}