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.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

public class Main
{ 
   //static long mod=(long)(1e+9 + 7);
   static long mod=(long)998244353;
   
   static int[] sieve;
   static ArrayList<Integer> primes;
   static long min=Long.MAX_VALUE;
   
   public static void main(String[] args) throws java.lang.Exception
   {	  	
	     fast s = new fast();
	     PrintWriter out=new PrintWriter(System.out);
	     
	     int t=s.nextInt();
	     StringBuilder fans=new StringBuilder("");
	    
	     while(t>0)
	    	 {
	    		 int n=s.nextInt();
	    		 int d=s.nextInt();
	    		 int a[]=new int[n];
	    		 for(int i=0;i<n;i++) a[i]=s.nextInt();
	    		 
	    		 for(int i=1;i<n;i++)
	    			 {
	    				 if(d==0) break;
	    				 int req=i;
	    				 int temp=Math.min(d/req, a[i]);
	    				 a[0]=a[0]+temp;
	    				 d=d-temp*i;
	    			 }
	    		 System.out.println(a[0]);
	    		 t--;
	    	 }
   }
  
 
 
static class fast {   
	    private InputStream i;
		private byte[]  buf = new byte[1024];
		private int curChar;
		
		private int numChars;
		
		//Return floor log2n
		public static long log2(long bits) // returns 0 for bits=0
			{
			    int log = 0;
			    if( ( bits & 0xffff0000 ) != 0 ) { bits >>>= 16; log = 16; }
			    if( bits >= 256 ) { bits >>>= 8; log += 8; }
			    if( bits >= 16  ) { bits >>>= 4; log += 4; }
			    if( bits >= 4   ) { bits >>>= 2; log += 2; }
			    return log + ( bits >>> 1 );
			}
		
		public static boolean next_permutation(int a[])
		   {
			   int i=0,j=0;int index=-1;	   
			   int n=a.length;
			   
			   for(i=0;i<n-1;i++)
				   if(a[i]<a[i+1]) index=i;
			   
			   if(index==-1) return false;
			   i=index;
 
			  
			   for(j=i+1;j<n && a[i]<a[j];j++);
 
			   int temp=a[i];
			   a[i]=a[j-1];
			   a[j-1]=temp;
			   	   
			   for(int p=i+1,q=n-1;p<q;p++,q--)
			   {
				   temp=a[p];
				   a[p]=a[q];
				   a[q]=temp;
			   }
			   
			   return true;
		   }
		   
		   
		public static void division(char ch[],int divisor)
		   {
			   int div=Character.getNumericValue(ch[0]); int mul=10;int remainder=0;
			   StringBuilder quotient=new StringBuilder("");
			   for(int i=1;i<ch.length;i++)
			   {
				   div=div*mul+Character.getNumericValue(ch[i]);	
				   if(div<divisor) {quotient.append("0");continue;}
				   quotient.append(div/divisor);
				   div=div%divisor;mul=10;
				   
			   } 
			   remainder=div;
			   while(quotient.charAt(0)=='0')quotient.deleteCharAt(0);	   
			   System.out.println(quotient+" "+remainder);	  
		   }
		
		public static void sieve(int size)
		{
			sieve=new int[size+1];
			
			primes=new ArrayList<Integer>();
			
			sieve[1]=1;
			
			for(int i=2;i*i<=size;i++)
			{
				if(sieve[i]==0)
				 {
					for(int j=i*i;j<size;j+=i) {sieve[j]=1;}
				 }
			}
			
			for(int i=2;i<=size;i++)
			{
				if(sieve[i]==0) primes.add(i);
			}
		}
		
		public static long pow(long n, long b, long MOD)
		   {
		       long x=1;long y=n; 
		       while(b > 0)
		       {
		           if(b%2 == 1)
		           {
		               x=x*y;
		               if(x>MOD) x=x%(MOD);
		           }
		           y = y*y;
		           if(y>MOD) y=y%(MOD); 
		           b >>= 1;
		       }
		       return x;
		   }
 
 
		public static long mod_inv(long n,long mod)
		{
			return pow(n,mod-2,mod);
		}
		
		//Returns index of highest number less than or equal to key
		 public static int upper(long[] a,int length,long key)
		 {
			    int low = 0;
		        int high = length-1;
		        int ans=-1;
		        
		        while (low <= high) {
		            int mid = (low + high) / 2;
		            if (key >= a[mid]) {
		                ans=mid;
		            	low = mid+1;
		            } else if(a[mid]>key){
		                high = mid - 1;
		            }
		        }
		        return ans;
		}
		
		//Returns index of least number greater than or equal to key
		 public static int lower(long[] a,int length,long key)
		 {
			    int low = 0;
		        int high = length-1;
		        int ans=-1;
		        
		        while (low <= high) {
		            int mid = (low + high) / 2;
		            if (key<=a[mid]) {
		                ans=mid;
		            	high = mid-1;
		            }
		            else{
		            		low=mid+1;
		            	}
		        }
		        return ans;
		} 
		   
		public long gcd(long r,long ans)
		{
			if(r==0) return ans;
			return gcd(ans%r,r);
		}
		public fast() {
			this(System.in);
		}
		public fast(InputStream is) {
			i = is;
		}
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = i.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
		public String nextString() {
     		int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
	}	
}