Codeforces Round #451 (Div. 2) B 拓展欧几里得

B. Proper Nutrition time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output

Vasya has n burles. One bottle of Ber-Cola costs a burles and one Bars bar costs b burles. He can buy any non-negative integer number of bottles of Ber-Cola and any non-negative integer number of Bars bars.

Find out if it’s possible to buy some amount of bottles of Ber-Cola and Bars bars and spend exactly n burles.

In other words, you should find two non-negative integers x and y such that Vasya can buy x bottles of Ber-Cola and y Bars bars and x·a + y·b = n or tell that it’s impossible.

Input

First line contains single integer n (1 ≤ n ≤ 10 000 000) — amount of money, that Vasya has.

Second line contains single integer a (1 ≤ a ≤ 10 000 000) — cost of one bottle of Ber-Cola.

Third line contains single integer b (1 ≤ b ≤ 10 000 000) — cost of one Bars bar.

Output

If Vasya can’t buy Bars and Ber-Cola in such a way to spend exactly n burles print «NO» (without quotes).

Otherwise in first line print «YES» (without quotes). In second line print two non-negative integers x and y — number of bottles of Ber-Cola and number of Bars bars Vasya should buy in order to spend exactly n burles, i.e. x·a + y·b = n. If there are multiple answers print any of them.

Any of numbers x and y can be equal 0.

Examples input

7
2
3

output

YES
2 1

input

100
25
10

output

YES
0 10

input

15
4
8

output

NO

input

9960594
2551
2557

output

YES
1951 1949

Note

In first example Vasya can buy two bottles of Ber-Cola and one Bars bar. He will spend exactly 2·2 + 1·3 = 7 burles.

In second example Vasya can spend exactly n burles multiple ways:

  • buy two bottles of Ber-Cola and five Bars bars;
  • buy four bottles of Ber-Cola and don’t buy Bars bars;
  • don’t buy Ber-Cola and buy 10 Bars bars.

In third example it’s impossible to but Ber-Cola and Bars bars in order to spend exactly n burles.

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <algorithm>
#include<fstream> 
#include <queue>
#include <stack>
#include <vector>
#include <map>
using namespace std;

typedef long long ll;
const int inf = 0x3f3f3f3f;
const ll llinf = 0x3f3f3f3f3f3f3f3f;
const int maxn = 1e5 + 5;;
const double PI = acos(-1);

ll e_gcd(ll a, ll b, ll &x, ll &y)
{
	if (b == 0)
	{
		x = 1;
		y = 0;
		return a;
	}
	ll ans = e_gcd(b, a%b, x, y);
	ll temp = x;
	x = y;
	y = temp - a / b*y;
	return ans;
}

ll cal(ll a, ll b, ll c)
{
	ll x, y;
	ll gcd = e_gcd(a, b, x, y);
	if (c%gcd != 0) return -1;
	x *= c / gcd;
	b /= gcd;
	if (b<0) b = -b;
	ll ans = x%b;
	if (ans < 0) ans += b;
	return ans;//返回的就是最小大于等于0的解
}

int main()
{	
	//freopen("Text.txt", "r", stdin);
	ll n,x,y,a,b;
	cin >> n;
	cin >> a;
	cin >> b;
	ll d = cal(a, b, n);
	if (d>=0)
	{
		if (d*a <= n)
			cout << "YES" << endl << d << " " << (n - a*d) / b << endl;
		else
			cout << "NO" << endl;
	}
	else
		cout << "NO" << endl;
	return 0;
}
    原文作者:B树
    原文地址: https://blog.csdn.net/weixin_38327682/article/details/78826865
    本文转自网络文章,转载此文章仅为分享知识,如有侵权,请联系博主进行删除。
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