CodeForces 414A Mashmokh and Numbers

最新推荐文章于 2025-03-16 13:53:08 发布

原创最新推荐文章于 2025-03-16 13:53:08 发布 · 664 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#codeforces #构造算法

构造算法专栏收录该内容

2 篇文章

订阅专栏

本文解析了一个CodeForces上的编程题目，该题目要求玩家通过策略选择一系列整数，使得游戏得分达到指定值。文章提供了AC代码及解题思路，帮助读者理解如何通过数学方法解决此类问题。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

链接：http://codeforces.com/problemset/problem/414/A

It's holiday. Mashmokh and his boss, Bimokh, are playing a game invented by Mashmokh.

In this game Mashmokh writes sequence of n distinct integers on the board. Then Bimokh makes several (possibly zero) moves. On the first move he removes the first and the second integer from from the board, on the second move he removes the first and the second integer of the remaining sequence from the board, and so on. Bimokh stops when the board contains less than two numbers. When Bimokh removes numbers x and y from the board, he gets gcd(x, y) points. At the beginning of the game Bimokh has zero points.

Mashmokh wants to win in the game. For this reason he wants his boss to get exactly k points in total. But the guy doesn't know how choose the initial sequence in the right way.

Please, help him. Find n distinct integers a₁, a₂, ..., a_n such that his boss will score exactly k points. Also Mashmokh can't memorize too huge numbers. Therefore each of these integers must be at most 10⁹.

Input

The first line of input contains two space-separated integers n, k (1 ≤ n ≤ 10⁵; 0 ≤ k ≤ 10⁸).

Output

If such sequence doesn't exist output -1 otherwise output n distinct space-separated integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹).

Sample test(s)

Input

5 2

Output

1 2 3 4 5

Input

5 3

Output

2 4 3 7 1

Input

7 2

Output

-1

Note

gcd(x, y) is greatest common divisor of x and y.

直接附上AC代码：

#include <iostream>
#include <cstdio>
#include <string>
#include <cmath>
#include <iomanip>
#include <ctime>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <set>
#include <map>
//#pragma comment(linker, "/STACK:102400000, 102400000")
using namespace std;
typedef unsigned int li;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
const double pi = acos(-1.0);
const double e = exp(1.0);
const double eps = 1e-8;
int n, k;

int main()
{
	ios::sync_with_stdio(false);
	while (~scanf("%d%d", &n, &k))
	{
		int cnt = n>>1;
		if (cnt>k || (cnt==0&&k!=0))
			printf("-1\n");
		else if (cnt==0 && k==0)
			printf("1\n");
		else
		{
			int i, extra=k-cnt+1;
			printf("%d %d", extra, 2*extra);
			for (i=2*extra+1; --cnt; i+=2)
				printf(" %d %d", i, i+1);
			if (n & 1)
				printf(" %d", i);
			printf("\n");
		}
	}
	return 0;
}