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: Accepted)

//set many funcs template
//Ver.20181228
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384
#define size 524288

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}
int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}
int chsortfnckj(const void *a,const void *b){if(*(char *)a<*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

void shuffledget(int x[],int n){
    srand(time(0));
    int i,b[524288],p,c;
    for(i=0;i<n;i++){
        b[i]=i;
    }
    for(i=n;i>=1;i--){
        p=rand()%i;
        c=b[i-1];b[i-1]=b[p];b[p]=c;
    }
    for(i=0;i<n;i++){
        scanf("%d",&x[b[i]]);
    }
}

int dx4[4]={1,-1,0,0};
int dy4[4]={0,0,1,-1};
int dx8[8]={-1,-1,-1,0,0,1,1,1};
int dy8[8]={-1,0,1,-1,1,-1,0,1};

long long search(long long x,long long a[],long long n){
    long long st=0,fi=n-1,te;
    while(st<=fi){
        te=(st+fi)/2;
        if(a[te]<x){st=te+1;}else{fi=te-1;}
    }
    return st;
}

void prarr(int arr[],int n){
  int i;
  for(i=0;i<n;i++){
    if(i){printf(" ");}
    printf("%d",arr[i]);
  }
  printf("\n");
  return;
}

typedef struct{
int val;
int node;
}sd;

int sdsortfnc(const void *a,const void *b){
if(((sd*)a)->val < ((sd*)b)->val){return -1;}
if(((sd*)a)->val > ((sd*)b)->val){return 1;}
return 0;
}

long long a[size];
long long n;

void dtag(long long x,long long c,long long *p,long long *q){
  long long st,fi,te;
  st=0;
  fi=inf;
  while(st<=fi){
    te=(st+fi)/2;
    (*p)=search(x-te,a,n);
    (*q)=search(x+te,a,n);
    if(a[(*q)]!=x+te){(*q)--;}
    if(((*q)-(*p)+1)==c){return;}
    if(((*q)-(*p)+1)<c){st=te+1;}
    if(((*q)-(*p)+1)>c){
      if(((*q)-(*p)+1)==c+1 && x-a[(*p)]==a[(*q)]-x){
        (*q)--;
        return;
      }
      fi=te-1;
    }
  }
}

int main(void){
    long long i,j,m,k,b,c,h,w,r=0,l,t;
    long long st,fi,te,q;
    long long ap,aq,bp,bq;
    long long rw[size],prw[size];
    long long res[size];
    sd query[size];
    scanf("%lld%lld",&n,&q);
    for(i=0;i<n;i++){
      scanf("%lld",&a[i]);
      if(i==0){
        rw[0]=a[i];
        prw[0]=0;
      }
      else{
        rw[i]=rw[i-1]+a[i];
        if(i%2){
          prw[i]=prw[i-1]+a[i];
        }
        else{
          prw[i]=prw[i-1];
        }
      }
    }
    a[n]=inf;
    for(i=0;i<q;i++){
      scanf("%lld",&query[i].val);
      query[i].node=i;
    }
    qsort(query,q,sizeof(query[0]),sdsortfnc);
    st=0;
    for(i=0;i<q;i++){
      //scanf("%lld",&k);
      k=query[i].val;
      if(k<a[0]){k=a[0];}
      //st=search(k,a,n);
      //if(a[st]!=k){st--;}
      //fi=n-1;
      //while(st<=fi){
      while(1){
        //te=(st+fi)/2;
        //dtag(k,n-1-te,&ap,&aq);
        dtag(k,n-1-st,&ap,&aq);
        //if(n-1-te==0){fi=te-1;}
        if(n-1-st==0){break;}
        //printf("<%lld %lld %lld>\n",te,ap,aq);
        //if(aq>=te){st=te+1;}
        //else{fi=te-1;}
        if(aq>=st){st++;}
        else{break;}
      }
      w=st;
      dtag(k,n-1-w,&ap,&aq);
      dtag(k,n-w,&bp,&bq);
      //printf("[%lld]\n",w);
      //printf("%lld %lld\n",ap,aq);
      //printf("%lld %lld\n",bp,bq);
      if(w==0){
        r=rw[n-1];
      }
      else{
        r=rw[n-1]-rw[w-1];
      }
      //printf("<%lld>\n",w);
      if(bq<w){
        w=bp-1;
      }
      else{
        w=bp-2;
      }
      //printf("[%lld]\n",w);
      if(w<0){
        r+=0;
      }
      else if(w%2){
        r+=prw[w];
      }
      else{
        r+=(rw[w]-prw[w]);
      }
      res[query[i].node]=r;
      //printf("%lld\n",r);
    }
    for(i=0;i<q;i++){
      printf("%lld\n",res[i]);
    }
    return 0;
}