【codeforce508C】. Anya and Ghosts

最新推荐文章于 2022-10-26 00:53:17 发布

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最新推荐文章于 2022-10-26 00:53:17 发布

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分类专栏： ==数学and思维== codeforces 其他and有趣的题目编程语言

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本文探讨了一个有趣的问题：如何计算在特定条件下所需的最小数量的蜡烛，以确保每次鬼来访时都有足够的蜡烛点亮。文章详细解释了输入参数的意义，并通过示例展示了算法的实现过程。

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Anya loves to watch horror movies. In the best traditions of horror, she will be visited by m ghosts tonight. Anya has lots of candles prepared for the visits, each candle can produce light for exactly t seconds. It takes the girl one second to light one candle. More formally, Anya can spend one second to light one candle, then this candle burns for exactly t seconds and then goes out and can no longer be used.

For each of the m ghosts Anya knows the time at which it comes: the i-th visit will happen w_i seconds after midnight, all w_i's are distinct. Each visit lasts exactly one second.

What is the minimum number of candles Anya should use so that during each visit, at least r candles are burning? Anya can start to light a candle at any time that is integer number of seconds from midnight, possibly, at the time before midnight. That means, she can start to light a candle integer number of seconds before midnight or integer number of seconds after a midnight, or in other words in any integer moment of time.

Input

The first line contains three integers m, t, r (1 ≤ m, t, r ≤ 300), representing the number of ghosts to visit Anya, the duration of a candle's burning and the minimum number of candles that should burn during each visit.

The next line contains m space-separated numbers w_i (1 ≤ i ≤ m, 1 ≤ w_i ≤ 300), the i-th of them repesents at what second after the midnight the i-th ghost will come. All w_i's are distinct, they follow in the strictly increasing order.

Output

If it is possible to make at least r candles burn during each visit, then print the minimum number of candles that Anya needs to light for that.

If that is impossible, print - 1.

Examples

Input

1 8 3
10

Output

Input

2 10 1
5 8

Output

Input

1 1 3
10

Output

-1

Note

Anya can start lighting a candle in the same second with ghost visit. But this candle isn't counted as burning at this visit.

It takes exactly one second to light up a candle and only after that second this candle is considered burning; it means that if Anya starts lighting candle at moment x, candle is buring from second x + 1 to second x + t inclusively.

In the first sample test three candles are enough. For example, Anya can start lighting them at the 3-rd, 5-th and 7-th seconds after the midnight.

In the second sample test one candle is enough. For example, Anya can start lighting it one second before the midnight.

In the third sample test the answer is - 1, since during each second at most one candle can burn but Anya needs three candles to light up the room at the moment when the ghost comes.

一个人要遇到m个鬼，遇到每个鬼的时间为w[i],蜡烛亮着的持续时间为t,遇到一个鬼至少要点燃r支蜡烛，
//点燃的时间不算燃烧时间，求他最少要带多少蜡烛，不存在就输出-1

code：

#include<cstdio>
#include<algorithm>
using namespace std;
#include<cstring> 
int num[1000];//某一时刻有多少蜡烛亮着
int w[1000];//每个鬼到的时间 
int main()
{
	int m,r,t;
	while(~scanf("%d%d%d",&m,&t,&r))
	{
		for(int i=1;i<=m;i++)
			scanf("%d",&w[i]);
			if(r>t){//持续时间比蜡烛数少，蜡烛未全部点燃，有的已经熄灭 
				printf("-1\n");
				continue;
			}
			memset(num,0,sizeof(num));
			int ans=0;//所需蜡烛数
			for(int i=1;i<=m;i++)//拜访每一个鬼 
			{
				for(int j=w[i]-1;num[w[i]]<r;j--){//从鬼来时的前一秒开始倒着点蜡烛 
				for(int k=j+1;k<=j+t;k++){//每个蜡烛持续时间段 
					if(k>=0)//j可能为0 
					 num[k]++; 
				}
				ans++;	
				} 
			 } 
			 printf("%d\n",ans);
	 } 
	return 0;
 }