The USA Construction Operation (USACO) recently ordered Farmer John to arrange a row of n haybale piles on the farm. The i-th pile contains a_i haybales. 

However, Farmer John has just left for vacation, leaving Bessie all on her own. Every day, Bessie the naughty cow can choose to move one haybale in any pile to an adjacent pile. Formally, in one day she can choose any two indices i and j (1 ≤ i, j ≤ n) such that |i-j|=1 and a_i>0 and apply a_i = a_i - 1, a_j = a_j + 1. She may also decide to not do anything on some days because she is lazy.

Bessie wants to maximize the number of haybales in pile 1 (i.e. to maximize a_1), and she only has d days to do so before Farmer John returns. Help her find the maximum number of haybales that may be in pile 1 if she acts optimally!

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases. Next 2t lines contain a description of test cases — two lines per test case.

The first line of each test case contains integers n and d (1 ≤ n,d ≤ 100) — the number of haybale piles and the number of days, respectively. 

The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 100) — the number of haybales in each pile.

Output

For each test case, output one integer: the maximum number of haybales that may be in pile 1 after d days if Bessie acts optimally.

Example

Input


3
4 5
1 0 3 2
2 2
100 1
1 8
0


Output


3
101
0

Note

In the first test case of the sample, this is one possible way Bessie can end up with 3 haybales in pile 1: 

  * On day one, move a haybale from pile 3 to pile 2 
  * On day two, move a haybale from pile 3 to pile 2 
  * On day three, move a haybale from pile 2 to pile 1 
  * On day four, move a haybale from pile 2 to pile 1 
  * On day five, do nothing 



In the second test case of the sample, Bessie can do nothing on the first day and move a haybale from pile 2 to pile 1 on the second day.
import java.io.*; 
import java.util.*; 
//import javafx.util.*; 
import java.math.*;
//import java.lang.*;
public class Main 
{ 
    
   // static int n;
   // static HashSet<Integer> adj[];
    
    // static boolean vis[];
   //  static long ans[];
   // static int arr[];
    static long mod=1000000007;
    static final long oo=(long)1e18;
    // static int n;
    public static void main(String[] args) throws IOException { 
    //    Scanner sc=new Scanner(System.in);
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        br = new BufferedReader(new InputStreamReader(System.in));
        int test=nextInt();
       // int test=1;
        outer: while(test--!=0){ 
            int n=nextInt();
            int d=nextInt();
            int arr[]=new int[n];
            for(int i=0;i<n;i++){
                arr[i]=nextInt();
            }
            int ans=arr[0];
            for(int i=1;i<n;i++){

                ans+=Math.min(d/i,arr[i]);
                
                d-=i*Math.min(d/i,arr[i]);
               // pw.println(ans+" "+d);
            }
            pw.println(ans);
        }   
        pw.close();
    }
   
    
static ArrayList<ArrayList<Integer>> permutation2(int[] a, int n) {
        ArrayList<ArrayList<Integer>> gen = new ArrayList<>();
        if(n == 1) {
            ArrayList<Integer> new_permutation = new ArrayList<>();
            new_permutation.add(a[n-1]);
            gen.add(new_permutation);
        } else {
            Iterator<ArrayList<Integer>> itr = permutation2(a, n-1).iterator();
            while(itr.hasNext()) {
                ArrayList<Integer> permutation = itr.next();
                // (create new permutation with this element in every position)
                for(int i = 0;i <= permutation.size();i++) {
                    ArrayList<Integer> new_permutation = new ArrayList<>(permutation);
                    new_permutation.add(i, a[n-1]);
                    gen.add(new_permutation);
                }
            }
        }
        return gen;
    }
    static void decToBinary(int n) 
    { 
        // array to store binary number 
        int[] binaryNum = new int[1000]; 
   
        // counter for binary array 
        int i = 0; 
        while (n > 0)  
        { 
            // storing remainder in binary array 
            binaryNum[i] = n % 2; 
            n = n / 2; 
            i++; 
        } 
   
        // printing binary array in reverse order 
        for (int j = i - 1; j >= 0; j--) 
            System.out.print(binaryNum[j]); 
        System.out.println();
    } 

    static long ncr(long n,long r){
        if(r==0)
            return 1;
        long val=ncr(n-1,r-1);
        val=(n*val)%mod;
        val=(val*modInverse(r,mod))%mod;
        return val;
    }

    static int find(ArrayList<Integer> a,int i){
        
        if(a.size()==0||i<0)return 0;
        ArrayList<Integer> l=new ArrayList<Integer>();
        ArrayList<Integer> r=new ArrayList<Integer>();
        for(int v:a){
            if((v&(1<<i))!=0)l.add(v);
            else r.add(v);
        }

        if(l.size()==0)return find(r,i-1);
        if(r.size()==0)return find(l,i-1);
        return Math.min(find(l,i-1),find(r,i-1))+(1<<i);
    }
    
    
    public static BufferedReader br;
    public static StringTokenizer st;
    public static String next() {
        while (st == null || !st.hasMoreTokens()) {
       try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }
        return st.nextToken();
    }
 
    public static Integer nextInt() {
        return Integer.parseInt(next());
    }
    public static Long nextLong() {
        return Long.parseLong(next());
    }
 
    public static Double nextDouble() {
        return Double.parseDouble(next());
    }
    // static class Pair{
    //     int x;int y;
    //     Pair(int x,int y,int z){
    //         this.x=x;
    //         this.y=y;
    //        // this.z=z;
    //      //   this.z=z;
    //       //  this.i=i;
    //     }
    // }
    // static class sorting implements Comparator<Pair>{
    //     public int compare(Pair a,Pair b){
    //         //return (a.y)-(b.y);
    //         if(a.y==b.y){
    //             return -1*(a.z-b.z);
    //         }
    //         return (a.y-b.y);
    //     }
   // }
    public static int[] na(int n)throws IOException{
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = nextInt();
        return a;
    }
    static class query implements Comparable<query>{
        int l,r,idx,block;
        static int len;
        query(int l,int r,int i){
            this.l=l;
            this.r=r;
            this.idx=i;
            this.block=l/len;
        }   
        public int compareTo(query a){
            return block==a.block?r-a.r:block-a.block;
        }
    }
    static class Pair implements Comparable<Pair>{
        int x;int y;
        Pair(int x,int y){
            this.x=x;
            this.y=y;
            //this.z=z;
        }   
        public int compareTo(Pair p){
            
            //return (x-p.x);
            if(x>p.x)
                return 1;
            if(x<p.x)
                return -1;
            return y-p.y;
            //return (x-a.x)>0?1:-1;
        }
    }
    // static class sorting implements Comparator<Pair>{  
    //     public int compare(Pair a1,Pair a2){  
    //         if(o1.a==o2.a)
    //             return (o1.b>o2.b)?1:-1;  
    //         else if(o1.a>o2.a)  
    //             return 1;  
    //         else  
    //             return -1;  
    //     }
    // }  
    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 ||  
            n % 3 == 0) 
            return false; 
      
        for (int i = 5; 
                 i * i <= n; i = i + 6) 
            if (n % i == 0 || 
                n % (i + 2) == 0) 
                return false; 
      
        return true; 
    } 
    static long gcd(long a, long b) { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }  
    // To compute x^y under modulo m 
    static long power(long x, long y, long m){ 
        if (y == 0) 
            return 1;      
        long p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    }
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
       static long modInverse(long n,long M){
        return fast_pow(n,M-2,M);
    }
    // (1,1)   

    //     (3,2)   (3,5)

} 