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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

class Main{
	static int[][] dp;
	static long ans = 0;
	static int H;
	static int W;
	static char[][] map;
	static int sub = 0;
	static boolean[][] used;
	static int[][] okblack;
	static ArrayList<Integer> bList;
	static int count;



	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		int N = sc.nextInt();
		int Q = sc.nextInt();
		int[] A = new int[N+1];
		long[] sum = new long[N+1];
		long[] oddevensum = new long[N+1];			//偶奇で分けた時の累積和

		for(int i = 1;i <= N;i++){
			A[i] = sc.nextInt();
			sum[i] = sum[i-1]+A[i];
			oddevensum[i] = A[i];
			if(i-2 > 0){
				oddevensum[i] += oddevensum[i-2];
			}
		}
		ArrayList<Pair> pairs = new ArrayList<Pair>();
		for(int i = 0;i < Q;i++){
			int o = sc.nextInt();
			Pair pair = new Pair();
			pair.from = o;
			pair.end = i;
			pairs.add(pair);
		}
		Collections.sort(pairs);
		

	//	System.out.println();
		long[] an = new long[Q];
		
		int y = 1;					//境界
		for(int i = 0; i < pairs.size();i++){
			int x = pairs.get(i).from;			//基準
			while(y <= N && A[y] < x){				//ここで固定を決める
				y++;
			}

			while(y <= N){
				int upper = N - y +1;			//y番目のカードを高橋は何枚目にとるか
				int lower = y - (lowerbond(Math.max(1, 2*x-A[y]),A))+1;		//y番目のカードをaokiは何枚目にとるか
				if(upper > lower){
					y++;
				}else{
					break;
				}
//				System.out.println(upper);
//				System.out.println(lower);

			}
//			System.out.println();
//			System.out.println("y " +y);

			long ans = sum[N] - sum[y-1];			//高橋だけがとる領域についての和
//			System.out.println("ans "+ans);
			int check = N - (N-y+1)*2;		
			if(check > 0){							//高橋と青木が交互にとる領域があるか判定
				ans += oddevensum[check];
			}
			an[pairs.get(i).end] = ans;
		}
//		System.out.println();

		for(int i = 0;i < Q;i++){
			System.out.println(an[i]);
		}
	}

	static int lowerbond(int k, int[] data){		//kより小さい最小の値をdataの中から探し、返す二分探索
		int min = -1;
		int max = data.length;

		while(max-min > 1){
			int mid = (max+min)/2;
			if(data[mid] >= k){
				max = mid;
			}else{
				min = mid;
			}
		}
//		System.out.println("return "+min);
		return max;
	}





	static void dfs(int y,int x,int color){
		//						System.out.println("y " + y + " x "+x  );



		if(map[y][x] == '.' && color == 0){
			//										System.out.println("ok");
			sub++;
		}
		int[] dx = {-1,1,0,0};
		int[] dy = {0,0,1,-1};
		for(int i = 0;i < 4;i++){
			if(x + dx[i] >= 0 && x + dx[i] < W && y + dy[i] >= 0 && y + dy[i] < H){
				if(color == 1){
					if(map[y+dy[i]][x+dx[i]] == '.' && !used[y+dy[i]][x+dx[i]]){
						used[y+dy[i]][x+dx[i]] = true;
						dfs(y+dy[i], x+dx[i], 0);
						//						used[y+dy[i]][x+dx[i]] = false;;

					}
				}else{
					if(map[y+dy[i]][x+dx[i]] == '#'&& !used[y+dy[i]][x+dx[i]]){
						map[y+dy[i]][x+dx[i]] = '¥';
						count++;
						used[y+dy[i]][x+dx[i]] = true;
						dfs(y+dy[i], x+dx[i], 1);

						//						used[y+dy[i]][x+dx[i]] = false;;

					}
				}
			}
		}

	}



}







class Pair implements Comparable{
	int from;		//p
	int end;		//y
	int num;
	int bango;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return from - otherpair.from;
	}
}