#include "peru.h"
#ifdef _LOCAL_
#include "grader.cpp"
#endif // _LOCAL_
#include <cassert>
#include <vector>
#include <deque>
#include <stack>
#include <queue>
#include <list>
#include <set>
using namespace std;
int rmq(int l, int r, const int *a)
{
int maxVal = a[l];
for(int i = l+1;i<=r;i++) maxVal = max(maxVal, a[i]);
return maxVal;
}
int convertToAns(const vector<long long> &dp)
{
long long p23 = 1, ans = 0;
const long long mod = 1e9 + 7;
for(int i = dp.size()-1;i>=0;i--)
{
ans = (ans + (dp[i]%mod)*p23)%mod;
p23 = (p23*23)%mod;
}
return ans;
}
int solve(int n, int k, int* a)
{
vector <long long> dp(n);
deque <int> dq;
vector <list<bool>> popTypes(n);
for(int i = 0;i<n;i++)
{
while(dq.empty()==false && i-dq.front()>=k)
{
popTypes[dq.front()].push_back(false);
dq.pop_front();
}
while(dq.empty()==false && a[dq.back()]<=a[i])
{
dq.pop_back();
if(dq.empty()==false) popTypes[dq.back()].push_back(true);
}
dq.push_back(i);
}
dq = {0};
dp[0] = a[0];
deque <pair <int, int>> valuesLeft;
stack <pair <int, int>> valuesRight;
long long prefMaxVal = a[0];
for(int i = 1;i<n;i++)
{
dp[i] = 1e18;
prefMaxVal = max(prefMaxVal, (long long)a[i]);
if(i<k) dp[i] = min(dp[i], prefMaxVal);
while(dq.empty()==false && i-dq.front()>=k)
{
int j = dq.front();
dq.pop_front();
if(dq.empty()==false)
{
if(valuesLeft.empty()==false && valuesLeft.front()==make_pair(j, dq.front()))
valuesLeft.pop_front();
}
}
while(dq.empty()==false && a[dq.back()]<=a[i])
{
if(dq.size()>=2)
{
if(valuesRight.empty()==false && valuesRight.top()==make_pair(*prev(prev(dq.end())), dq.back()))
valuesRight.pop();
}
dq.pop_back();
}
if(dq.empty()==false)
{
long long currVal = dp[dq.back()] + a[i];
if(popTypes[dq.back()].empty()==false && popTypes[dq.back()].front()==false)
{
while(valuesLeft.empty()==false && dp[valuesLeft.back().first]+a[valuesLeft.back().second]>=currVal)
valuesLeft.pop_back();
valuesLeft.emplace_back(dq.back(), i);
popTypes[dq.back()].pop_front();
}
else
{
if(valuesRight.empty()==true || dp[valuesRight.top().first]+a[valuesRight.top().second]>=currVal)
valuesRight.emplace(dq.back(), i);
if(popTypes[dq.back()].empty()==false) popTypes[dq.back()].pop_front();
}
}
dq.push_back(i);
int last = max(i-k, 0);
if(dq.front()>last) dp[i] = min(dp[i], dp[last] + a[dq.front()]);
if(valuesLeft.empty()==false) dp[i] = min(dp[i], dp[valuesLeft.front().first] + a[valuesLeft.front().second]);
if(valuesRight.empty()==false) dp[i] = min(dp[i], dp[valuesRight.top().first] + a[valuesRight.top().second]);
}
return convertToAns(dp);
}
