#include "peru.h"
#include<bits/stdc++.h>
using namespace std;
using i64 = long long;
//#define int i64
#define vi vector<int>
#define vvi vector<vi>
#define vb vector<bool>
#define se second
#define fi first
#define pii pair<int, int>
#define sz(x) (int)(x).size()
const int MOD = 1e9 + 7;
const int B = 23;
const int MAXN = 25e5 + 5;
i64 pw[MAXN];
inline int hashx(int n, vector<i64> &x){
int ret = 0;
for(int i = 0; i < n; i++){
//cout << "i: " << i << " x: " << x[i] << "\n";
x[i] %= MOD;
i64 val = (x[i] * pw[n - 1 - i]) % MOD;
ret = (ret + val) % MOD;
}
return ret;
}
int solve(int n, int k, int *s){
pw[0] = 1;
for(int i = 1; i <= n; i++){
pw[i] = (pw[i - 1] * B) % MOD;
}
vector<i64> dp(n);
dp[0] = s[0];
deque<int> dq;
multiset<i64> ms;
dq.emplace_back(0);
ms.emplace(dp[0] + s[1]);
for(int i = 1; i < k; i++){
dp[i] = max(dp[i - 1], (i64)s[i]);
if(i + 1 < n){
while(!dq.empty() && s[dq.back() + 1] < s[i + 1]){
int idx = dq.back();
ms.erase(ms.find(dp[idx] + s[idx + 1]));
dq.pop_back();
}
dq.emplace_back(i);
ms.emplace(dp[i] + s[i + 1]);
}
}
for(int i = k; i < n; i++){
dp[i] = dp[i - 1] + s[i];
while(!dq.empty() && dq.front() < i - k){
int idx = dq.front();
ms.erase(ms.find(dp[idx] + s[idx + 1]));
dq.pop_front();
}
dp[i] = min(dp[i], *ms.begin());
if(i + 1 < n){
while(!dq.empty() && s[dq.back() + 1] < s[i + 1]){
int idx = dq.back();
ms.erase(ms.find(dp[idx] + s[idx + 1]));
dq.pop_back();
}
dq.emplace_back(i);
ms.emplace(dp[i] + s[i + 1]);
}
}
return hashx(n, dp);
}
/*
signed main(){
ios_base::sync_with_stdio(false); cin.tie(0);
int n, k;
cin >> n >> k;
int s[n];
for(int i = 0; i < n; i++){
cin >> s[i];
}
cout << solve(n, k, s) << "\n";
return 0;
}
*/
