Problem:
Score : 500 points

Problem Statement

There are N cards. The i-th card has an integer A_i written on it.
For any two cards, the integers on those cards are different.

Using these cards, Takahashi and Aoki will play the following game:

Aoki chooses an integer x.

Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner:

Takahashi should take the card with the largest integer among the remaining card.

Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards.

The game ends when there is no card remaining.

You are given Q candidates for the value of x: X_1, X_2, ..., X_Q.
For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i.

Constraints

2 \leq N \leq 100 000

1 \leq Q \leq 100 000

1 \leq A_1 < A_2 < ... < A_N \leq 10^9

1 \leq X_i \leq 10^9 (1 \leq i \leq Q)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
A_1 A_2 ... A_N
X_1
X_2
:
X_Q

Output

Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i.

Sample Input 1

5 5
3 5 7 11 13
1
4
9
10
13

Sample Output 1

31
31
27
23
23

For example, when x = X_3(= 9), the game proceeds as follows:

Takahashi takes the card with 13.

Aoki takes the card with 7.

Takahashi takes the card with 11.

Aoki takes the card with 5.

Takahashi takes the card with 3.

Thus, 13 + 11 + 3 = 27 should be printed on the third line.

Sample Input 2

4 3
10 20 30 40
2
34
34

Sample Output 2

70
60
60

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#if 0
cat <<EOF >mistaken-paste
#endif
// thanks for @rsk0315_h4x

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"
#define _USE_MATH_DEFINES

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>

#define BIG 2000000007
#define VERYBIG 2000000000000007LL

#define MOD 1000000007
#define FOD  998244353
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 1000000

#ifdef __cplusplus
#include <queue>
#include <stack>
#include <tuple>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <functional>
#include <array>

using std::queue;
using std::priority_queue;
using std::stack;
using std::tuple;
using std::set;
using std::map;
using std::vector;
using std::greater;
using std::pair;
using std::string;
using std::get;

template <typename T, typename U>
pair<T, U> operator+(pair<T, U> l, pair<T, U> r) {
	return pair<T, U>(l.first + r.first, l.second + r.second);
}

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	sll a;
	sll b;
	sll c;
} hwllc;

typedef struct {
	hwll a;
	hwll b;
} linell;

ull n, m;
ull h, w;
ull k;
ull q;
sll va, vb, vc, vd, ve, vf;
ull ua, ub, uc, ud, ue, uf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
char ch, dh;

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull udiff (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sdiff (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#define BEGCMP(NAME) int32_t NAME (const void *left, const void *right)
#define DEFLR(TYPE) TYPE l=*(TYPE*)left,r=*(TYPE*)right
#define CMPRET(L, R) if((L)<(R))return-1;if((L)>(R))return+1

// int32_t pullcomp (const void *left, const void *right) {
// 	ull l = *(ull*)left;
// 	ull r = *(ull*)right;
// 	if (l < r) {
// 		return -1;
// 	}
// 	if (l > r) {
// 		return +1;
// 	}
// 	return 0;
// }
BEGCMP(pullcomp){
	DEFLR(ull);
	CMPRET(l, r);
	return 0;
}
BEGCMP(prevcomp){
	DEFLR(ull);
	CMPRET(r, l);
	return 0;
}
BEGCMP(psllcomp){
	DEFLR(sll);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pcharcomp){
	DEFLR(char);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pdoublecomp){
	DEFLR(double);
	CMPRET(l, r);
	return 0;
}

int32_t pstrcomp (const void *left, const void *right) {
	char* l = *(char**)left;
	char* r = *(char**)right;

	return strcmp(l, r);
}

BEGCMP(phwllABcomp){
	DEFLR(hwll);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwllREVcomp){
	DEFLR(hwll);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	return 0;
}
BEGCMP(ptriplecomp){
	DEFLR(hwllc);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleREVcomp){
	DEFLR(hwllc);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	CMPRET(l.c, r.c);
	return 0;
}

int32_t pquadcomp (const void *left, const void *right) {
	linell l = *(linell*)left;
	linell r = *(linell*)right;

	sll ac = phwllABcomp(&(l.a), &(r.a));
	if (ac) return ac;
	sll bc = phwllABcomp(&(l.b), &(r.b));
	if (bc) return bc;

	return 0;
}

bool isinrange (sll left, sll x, sll right) {
	return (left <= x && x <= right);
}

bool isinrange_soft (sll left, sll x, sll right) {
	return (left <= x && x <= right) || (left >= x && x >= right);
}

sll a[N_MAX + 5];
// ull a[N_MAX + 5];
// sll a[3001][3001];
sll b[N_MAX + 5];
// ull b[N_MAX + 5];
// sll b[3001][3001];
sll c[N_MAX + 5];
ull d[N_MAX + 5];
sll e[N_MAX];
// char s[N_MAX + 1];
char s[3010][3010];
char t[N_MAX + 1];
// char t[3010][3010];
char u[N_MAX + 1];
hwll xy[N_MAX + 5];
hwllc tup[N_MAX + 5];
sll table[3005][3005];
// here we go

ull gin[N_MAX];
ull vvv (ull v, ull p) {
	e[v] = 1;
	for (sll i = gin[v]; i < gin[v + 1]; i++) {
		ull u = xy[i].b;
		if (u == p) continue;
		d[u] = d[v] + 1;
		e[v] += vvv(u, v);
	}
	return e[v];
}

sll dp[5005][2][5005];
ull dfs (ull v, ull p) {
	sll tmp[2][e[v]];

	for (sll i = 0; i <= n; i++) {
		dp[v][0][i] = dp[v][1][i] = VERYBIG;
	}
	dp[v][(c[v] < 0) ? 1 : 0][0] = c[v];
	// printf("%lld %lld: %lld\n", v, 0LL, c[v]);
	ull maxv = 1;
	for (sll i = gin[v]; i < gin[v + 1]; i++) {
		ull u = xy[i].b;
		if (u == p) continue;
		ull maxu = dfs(u, v);

		for (sll x = 0; x < e[v]; x++) tmp[0][x] = tmp[1][x] = VERYBIG;
		for (sll x = 0; x <= maxv - 1; x++) {
			for (sll y = 0; y <= maxu - 1; y++) {

				for (sll z1 = 0; z1 <= 1; z1++) {

					for (sll z2 = 0; z2 <= 1; z2++) {

						tmp[z1 | z2][x + y] = smin(tmp[z1 | z2][x + y], dp[v][z1][x] + dp[u][z2][y]);
						// printf("%lld+%lld [%lld] <- %lld\n", x, y, (z1 | z2), tmp[z1 | z2][x + y]);
						if ((!z2 && dp[u][z2][y] != VERYBIG) || dp[u][z2][y] < 0) {
							tmp[z1][x + y + 1] = smin(tmp[z1][x + y + 1], dp[v][z1][x]);
							// printf("%lld+%lld+1 [%lld] <- %lld (%lld %lld %lld: %lld)\n", x, y, z1, tmp[z1][x + y + 1], u, z2, y, dp[u][z2][y]);
						}
					}
				}

			}
		}
		for (sll x = 0; x < e[v]; x++) {
			dp[v][0][x] = tmp[0][x];
			dp[v][1][x] = tmp[1][x];
			// printf("%lld/%lld: %lld, %lld\n", v, x, dp[v][0][x], dp[v][1][x]);
		}
		maxv += maxu;
	}
	return maxv;
}

ull p[N_MAX], size[N_MAX];

void uf_init (ull n) {
	for (ull i = 0; i < n; i++) {
		p[i] = i;
		size[i] = 1;
	}
}
ull uf_find (ull x) {
	if (p[x] == x) return x;
	return p[x] = uf_find(p[x]);
}
bool uf_union (ull a, ull b) {
	a = uf_find(a);
	b = uf_find(b);
	if (a == b) return false;

	if (size[a] < size[b]) {
		a ^= b;
		b ^= a;
		a ^= b;
	}
	p[b] = a;
	size[a] += size[b];
	return true;
}

ull acc[N_MAX];
ull bcc[N_MAX];

ull solve () {
	sll i, j, ki, li;
	// ull result = 0;
	sll result = 0;
	double dresult = 0;
	// ull maybe = 0;
	sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	sll item;
	ull *dpcell;

	for (i = 0; i < n; i++) {
		if (i < 2) {
			acc[i] = a[i];
		} else {
			acc[i] = acc[i - 2] + a[i];
		}
	}
	bcc[n - 1] = a[n - 1];
	for (i = n - 2; i >= 0; i--) {
		bcc[i] = bcc[i + 1] + a[i];
	}

	for (sll i = 0; i < q; i++) {
		xy[i] = (hwll){-c[i], i};
	}
	qsort(xy, q, sizeof(hwll), phwllABcomp);

	sll first = n - 1, last = n - 1;
	// for (i = 0; i < n; i++) {
	// 	if (sdiff(a[i], -xy[0].a) < sdiff(a[first], -xy[0].a)) first = i;
	// }
	// last = i;
	ull len = 1;
	for (i = 0; i < q; i++) {
		sll x = -xy[i].a;
		while (first > 0) {
			if (sdiff(a[first - 1], x) <= sdiff(a[last], x)) {
				first--;
				last--;
			} else {
				break;
			}
		}

		while (last + len < n - 1) {
			bool isl;
			if (!first) isl = false;
			else if (last == n - 1) isl = true;
			else if (a[first - 1] <= a[last + 1]) isl = true;
			else isl = false;

			if (isl) {
				// if (last + len + 1 >= n - 1) break;
				first--;
			} else {
				// if (last + len + 2 >= n - 1) break;
				last++;
			}
			len++;
		}

		// printf("%lld ~ %lld\n", first, last);

		c[xy[i].b] = ((len * 2 < n) ? acc[n - len * 2 - 1] : 0) + bcc[n - len];

	}

	for (i = 0; i < q; i++) {
		printf("%lld\n", c[i]);
	}

	// printf("%lld\n", result);
	// printf("%.15lf\n", dresult);
	// puts(s);

	return 0;

	success:
	puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	// puts("Yay!");
	return 0;

	fail:
	// puts("NO");
	// puts("No");
	// puts("0");
	puts("-1");
	// puts("-1 -1 -1");
	// puts("Impossible");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;



	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &n, &m);
	// scanf("%llu", &k, &n, &m);
	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &q);
	// scanf("%s", s);
	// scanf("%lld%lld", &va, &vb, &vc, &vd);
	// scanf("%llu%llu%llu", &ua, &ub, &uc, &ud);
	// scanf("%s", t);
	// scanf("%lld", &m);
	for (i = 0; i < n; i++) {
		// scanf("%lld%lld", &xy[i].a, &xy[i].b);
		// scanf("%lld%lld%lld", &tup[i].a, &tup[i].b, &tup[i].c);
		scanf("%lld", &a[i]);
		// scanf("%lld", &b[i]);
		// scanf("%lld", &c[i]);
		// scanf("%lld", &d[i]);
		// a[i]--;
		// b[i]--;
		// c[i]--;
		// d[i]--;
		// xy[i].a--;
		// xy[i].b--;
		// tup[i].a--;
		// tup[i].b--;
	}
	// for (i = 0; i < n - 1; i++) {
	// 	scanf("%lld%lld", &a[i], &b[i]);
	// 	a[i]--;
	// 	b[i]--;
	// }
	// scanf("%llu", &m, &k);
	// scanf("%llu", &q);
	// scanf("%s", s);
	// for (i = 0; i < n; i++) {
	// 	scanf("%lld", &a[i]);
	// 	// scanf("%lld", &b[i]);
	// 	// b[i]--;
	// 	// c[i]--;
	// }
	// scanf("%llu", &q);

	for (i = 0; i < q; i++) {
		// scanf("%lld%lld", &xy[i].a, &xy[i].b);
		scanf("%lld", &c[i]);
		// xy[i].a--;
		// xy[i].b--;
	}

	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < n; j++) {
	// 		scanf("%lld", &table[i][j]);
	// 		// table[i][j]--;
	// 	}
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%s", s[i]);
	// }
	// scanf("%llu", &q);

	solve();

	return 0;
}