Problem: There are N panels arranged in a row in Takahashi's house, numbered 1 through N. The i-th panel has a number A_i written on it. Takahashi is playing by throwing balls at these panels.

Takahashi threw a ball K times. Let the panel hit by a boll in the i-th throw be panel p_i. He set the score for the i-th throw as i \times A_{p_i}.

He was about to calculate the total score for his throws, when he realized that he forgot the panels hit by balls, p_1,p_2,...,p_K. The only fact he remembers is that for every i (1 ≦ i ≦ K-1), 1 ≦ p_{i+1}-p_i ≦ M holds. Based on this fact, find the maximum possible total score for his throws.

Constraints

* 1 ≦ M ≦ N ≦ 100,000
* 1 ≦ K ≦ min(300,N)
* 1 ≦ A_i ≦ 10^{9}

Input

The input is given from Standard Input in the following format:


N M K
A_1 A_2 … A_N


Output

Print the maximum possible total score for Takahashi's throws.

Examples

Input

5 2 3
10 2 8 10 2


Output

56


Input

5 5 2
5 2 10 5 9


Output

28


Input

10 3 5
3 7 2 6 9 4 8 5 1 1000000000


Output

5000000078

Solution (in CPP):

Solution:
// #pragma GCC target("avx2")  // CPU 処理並列化
// #pragma GCC optimize("O3")  // CPU 処理並列化
// #pragma GCC optimize("unroll-loops")  // 条件処理の呼び出しを減らす
#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<deque>
#include<stack>
#include<string>
#include<string.h>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#include<stdlib.h>
#include<cassert>
#include<time.h>
#include<bitset>
#include<numeric>
using namespace std;
const long long mod=998244353;
const long long inf=mod*mod;
const long long d2=(mod+1)/2;
const double EPS=1e-10;
const double INF=1e+10;
const double PI=acos(-1.0);
const int C_SIZE = 3121000;
long long fact[C_SIZE];
long long finv[C_SIZE];
long long inv[C_SIZE];
long long Comb(int a,int b){
 	if(a<b||b<0)return 0;
 	return fact[a]*finv[b]%mod*finv[a-b]%mod;
}
void init_C(int n){
	fact[0]=finv[0]=inv[1]=1;
	for(int i=2;i<n;i++){
		inv[i]=(mod-(mod/i)*inv[mod%i]%mod)%mod;
	}
	for(int i=1;i<n;i++){
		fact[i]=fact[i-1]*i%mod;
		finv[i]=finv[i-1]*inv[i]%mod;
	}
}
long long pw(long long a,long long b){
	if(a<0LL)return 0;
	if(b<0LL)return 0;
	long long ret=1;
	while(b){
		if(b%2)ret=ret*a%mod;
		a=a*a%mod;
		b/=2;
	}
	return ret;
}
int ABS(int a){return max(a,-a);}
long long ABS(long long a){return max(a,-a);}
double ABS(double a){return max(a,-a);}
// ここから編集しろ
long long p[110000];
long long dp[310][110000];
int main(){
	int a,b,c;scanf("%d%d%d",&a,&b,&c);
	for(int i=0;i<a;i++)scanf("%lld",p+i);
	for(int i=0;i<a;i++)dp[1][i]=p[i];
	for(int i=2;i<=c;i++){
		deque<pair<long long,int> > Q;
		for(int j=0;j<a;j++){
			while(Q.size()&&Q.front().second<j-b){
				Q.pop_front();
			}
			if(Q.size()==0)dp[i][j]=-inf;
			else dp[i][j]=Q.front().first+p[j]*i;
			while(Q.size()&&Q.back().first<=dp[i-1][j]){
				Q.pop_back();
			}
			Q.push_back(make_pair(dp[i-1][j],j));
		}
	}
	long long ret=0;
	for(int i=0;i<a;i++)ret=max(ret,dp[c][i]);
	printf("%lld\n",ret);
}