#include #include using namespace std; #define rep(i,n) for(long long i = 0; i < (long long)(n); i++) template bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); } template bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } using ll = long long; using vll = vector; using vvll = vector; using P = pair; static const long long INF = 1e18; /*****************/ // Dictionary /*****************/ // Nはバケット数 template class FID { static const int bucket = 512, block = 16; // 整数iのpopcountをO(1)で求めるためのテーブル // popcount[i] = __builtin_popcount(i), i<65536 static char popcount[]; // B[i]: s[0:512*i)のビット1の総数 int n, B[N/bucket+10]; // bs[i]: s[16*i:16*(i+1)]のビット列そのもの unsigned short bs[N/block+10] = {}; // b[i]: s[i/32*512:i/32*512+i%32*32)のビット1の総数 // bs[i]を512bitずつリセットしながら、累積和を取ってる感じ。 unsigned short b[N/block+10] = {}; public: FID(){} FID(int n, bool s[]) : n(n) { if(!popcount[1]) for (int i = 0; i < (1<1) { md = (lb+ub)>>1; if(count(val,md) >= i) ub = md; else lb = md; } return ub-1; } int select(bool val, int i, int l) { return select(val,i+count(val,l)); } }; template char FID::popcount[1<::block]; /*****************/ // Wavelet Matrix /*****************/ // 長さNで、値域[0, m=2^D)の整数を管理する template class wavelet { int n, zs[D]; FID dat[D]; T raw_data[D+1][N] = {}; T sum_data[D+1][N+1] = {}; public: wavelet(int n, T seq[]) : n(n) { T l[N] = {}, r[N] = {}; bool b[N] = {}; memcpy(raw_data[0], seq, sizeof(T)*n); for (int d = 0; d < D; d++) { int lh = 0, rh = 0; for (int i = 0; i < n; i++) { b[i] = (raw_data[d][i]>>(D-d-1))&1; if(b[i]) r[rh++] = raw_data[d][i]; else l[lh++] = raw_data[d][i]; } dat[d] = FID(n,b); zs[d] = lh; swap(l,raw_data[d+1]); memcpy(raw_data[d+1]+lh, r, rh*sizeof(T)); } rep(d, D+1) rep(i, N) sum_data[d][i+1] = sum_data[d][i] + raw_data[d][i]; } // 深さdでの列の[l, r)での累積和を求める T getSum(int d, int l, int r) { return sum_data[d][r] - sum_data[d][l]; } // rank: 区間[0,r)にあるvalの個数 // O(log m) int count(T val, int l, int r) { for (int d = 0; d < D; d++) { // ここで[l, r)にxのd桁目までが全て入っていることを保証(d>0) bool b = (val>>(D-d-1))&1; l = dat[d].count(b,l)+b*zs[d]; r = dat[d].count(b,r)+b*zs[d]; } return r-l; } int count(T val, int r) { return count(val,0,r); } // k is 0-indexed!!!! // kth_number: 区間[l,r)でk番目に大きい数 // O(log m) T kth_number(int l, int r, int k) { if(r-l <= k or k < 0) return -1; T ret = 0; for (int d = 0; d < D; d++) { int lc = dat[d].count(1,l), rc = dat[d].count(1,r); // lc - rc = [l, r)で立っている1の数 if(rc-lc > k) { // 1の数にkが収まっていれば l = lc+zs[d], r = rc+zs[d]; // 1側に遷移 ret |= 1ULL<<(D-d-1); } else { // 0側ならば k -= rc-lc; // 1側にあった数だけkを削って次へ l -= lc, r -= rc; } } return ret; } // number of elements in [l,r) in [a,b) // O(log m) int freq_dfs(int d, int l, int r, T val, T a, T b) { if(l == r) return 0; if(d == D) return (a <= val and val < b)? r-l: 0; T nv = 1ULL<<(D-d-1)|val, nnv = ((1ULL<<(D-d-1))-1)|nv; if(nnv < a or b <= val) return 0; if(a <= val and nnv < b) return r-l; int lc = dat[d].count(1,l), rc = dat[d].count(1,r); return freq_dfs(d+1,l-lc,r-rc,val,a,b)+ freq_dfs(d+1,lc+zs[d],rc+zs[d],nv,a,b); } int freq(int l, int r, T a, T b) { return freq_dfs(0,l,r,0,a,b); } // get sum of elements in [l,r) in [a,b) // O(log m) T sum_dfs(int d, int l, int r, T val, T a, T b) { // Wavelet Matrixの深さdで、 // [l, r)が[val, nv) = [val, val+(1ll<<(D-d)))の値域を表現している時、 // [a, b)の値域のものの和は? if(l == r) return 0; // valは無いので0を返す if(d == D) return (a <= val and val < b)? (r-l)*val: 0; // 深さDでは全部の値が同じなので、そのままかけて返す T nv = 1ULL<<(D-d-1)|val, nnv = ((1ULL<<(D-d-1))-1)|nv; if(nnv < a or b <= val) // どんなに1を選んでもaに満たなかったり、すでに最大を超えていたら0 return 0; if (a <= val and nnv < b) // これからどう選んでも a <= [l, r) < bの場合、累積和を返す return getSum(d, l, r); int lc = dat[d].count(1,l), rc = dat[d].count(1,r); return sum_dfs(d+1,l-lc,r-rc,val,a,b)+ sum_dfs(d+1,lc+zs[d],rc+zs[d],nv,a,b); } T sum(int l, int r, T a, T b) { return sum_dfs(0,l,r,0,a,b); } }; #define MAXN 100010 #define MAXK 30 int main(void) { ll n, k; cin >> n >> k; assert(1<=k&&k<=n&&n<=100000); ll a[MAXN]; rep(i, n) { cin >> a[i]; assert(1<=a[i]&&a[i]<=1e9); } wavelet w(n, a); ll ret = INF; rep(i, n-k+1) { ll val = w.kth_number(i, i+k, k/2); ll less_than_sum = w.sum(i, i+k, 0, val); ll more_than_sum = w.sum(i, i+k, val+1, (1ll<