CF985C Liebig's Barrels 贪心第二十

You have m = n·k wooden staves. The i-th stave has length ai. You have to assemble n barrels consisting of k staves each, you can use any k staves to construct a barrel. Each stave must belong to exactly one barrel.

Let volume vj of barrel j be equal to the length of the minimal stave in it.

$\text{[math]}$

You want to assemble exactly n barrels with the maximal total sum of volumes. But you have to make them equal enough, so a difference between volumes of any pair of the resulting barrels must not exceed l, i.e. |vx - vy| ≤ l for any 1 ≤ x ≤ n and 1 ≤ y ≤ n.

Print maximal total sum of volumes of equal enough barrels or 0 if it's impossible to satisfy the condition above.

Input

The first line contains three space-separated integers n, k and l (1 ≤ n, k ≤ 105, 1 ≤ n·k ≤ 105, 0 ≤ l ≤ 109).

The second line contains m = n·k space-separated integers a1, a2, ..., am (1 ≤ ai ≤ 109) — lengths of staves.

Output

Print single integer — maximal total sum of the volumes of barrels or 0 if it's impossible to construct exactly n barrels satisfying the condition |vx - vy| ≤ l for any 1 ≤ x ≤ n and 1 ≤ y ≤ n.

Examples

input

Copy

4 2 1
2 2 1 2 3 2 2 3

output

Copy

input

Copy

2 1 0
10 10

output

Copy

input

Copy

1 2 1
5 2

output

Copy

input

Copy

3 2 1
1 2 3 4 5 6

output

Copy

Note

In the first example you can form the following barrels: [1, 2], [2, 2], [2, 3], [2, 3].

In the second example you can form the following barrels: [10], [10].

In the third example you can form the following barrels: [2, 5].

In the fourth example difference between volumes of barrels in any partition is at least 2 so it is impossible to make barrels equal enough.

题意：输入 n k l 你要做n个桶，每个桶需要k个木板，用木板拼好的桶相互之间体积的差距<=l，桶的体积大小就是最短的那根木板的长度大小。

第二行共n*k个数，分别表示n*k个木板的长度。

开始自己的思路是对的，但是中间的具体细节写错了，wa了好几发

然后看的别人的博客才写出来的

http://www.mamicode.com/info-detail-2309549.html

分析：

先对边排个序

不存在的情况，就是a[n]-a[1]>l，那就是不存在，因为要是差距尽可能小，前n小的都分别作为n个桶的一块木板，那么这之中最大的差距就是a[n]-a[1]，要是a[n]-a[1]都满足条件（<=l）了，那就满足条件了。

其次，要使体积和最大输出体积和，我毛想想觉得s=a[1]+……a[n]，结果WA了，引起了我的深思。

因为：

eg：4 3 17

1 2 3 5 9 13 18 21 22 23 25 26

它可以这样组3组：

18 25 26

13 22 23

1 2 3

5 9 21

这样体积为1+5+13+18=37，不是简单地1 +2 +3 +5=11

所以我的思路：先要找到最大的满足条件的数，可以用二分找更快，在这组样例中，是18，它-a[1]<=l，

那么从最后开始去k-1个和18拼，s+=18，再下一个数13（25 26），再从最后找k-1个数（22 23），

再下一个数9，发现再k-1个数不够了，那就从头开始找了，（1 2 3）一组，在去（5 9 13）时，发现13

已经被取走，那就s+=5就可以了。

#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
#define debug(a) cout << #a << " " << a << endl
using namespace std;
const int maxn = 1e5 + 10;
const int mod = 1e9 + 7;
typedef long long ll;
ll a[maxn];
int main(){
    std::ios::sync_with_stdio(false);
    ll n, k, m;
    while( cin >> n >> k >> m ) {
        for( ll i = 1; i <= n*k; i ++ ) {
            cin >> a[i];
        }
        sort( a + 1, a + n*k + 1 );
        ll num = -1;
        for( ll i = n*k; i >= n; i -- ) {
            if( a[i] - a[1] <= m ) {
                num = i;
                break;
            }
        }
        if( num == -1 ) {
            cout << 0 << endl;
            continue;
        }
        ll sum = 0, j = num, t = 0 ;
        for( ll i = n*k ; i - ( k-1 ) > num; i = i - ( k-1 ) ) {
            sum += a[j--];
            t ++;
        }
        for( ll i = 1; i < num - t + 1; i += k ) {
            sum += a[i];
        }
        cout << sum << endl;
    }
    return 0;
}

CF985C Liebig's Barrels 贪心 第二十

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CF985C Liebig's Barrels 贪心第二十