Problem: A mad scientist Dr.Jubal has made a competitive programming task. Try to solve it!

You are given integers n,k. Construct a grid A with size n × n consisting of integers 0 and 1. The very important condition should be satisfied: the sum of all elements in the grid is exactly k. In other words, the number of 1 in the grid is equal to k.

Let's define:

  * A_{i,j} as the integer in the i-th row and the j-th column. 
  * R_i = A_{i,1}+A_{i,2}+...+A_{i,n} (for all 1 ≤ i ≤ n). 
  * C_j = A_{1,j}+A_{2,j}+...+A_{n,j} (for all 1 ≤ j ≤ n). 
  * In other words, R_i are row sums and C_j are column sums of the grid A. 
  * For the grid A let's define the value f(A) = (max(R)-min(R))^2 + (max(C)-min(C))^2 (here for an integer sequence X we define max(X) as the maximum value in X and min(X) as the minimum value in X). 



Find any grid A, which satisfies the following condition. Among such grids find any, for which the value f(A) is the minimum possible. Among such tables, you can find any.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. Next t lines contain descriptions of test cases.

For each test case the only line contains two integers n, k (1 ≤ n ≤ 300, 0 ≤ k ≤ n^2).

It is guaranteed that the sum of n^2 for all test cases does not exceed 10^5.

Output

For each test case, firstly print the minimum possible value of f(A) among all tables, for which the condition is satisfied.

After that, print n lines contain n characters each. The j-th character in the i-th line should be equal to A_{i,j}.

If there are multiple answers you can print any.

Example

Input


4
2 2
3 8
1 0
4 16


Output


0
10
01
2
111
111
101
0
0
0
1111
1111
1111
1111

Note

In the first test case, the sum of all elements in the grid is equal to 2, so the condition is satisfied. R_1 = 1, R_2 = 1 and C_1 = 1, C_2 = 1. Then, f(A) = (1-1)^2 + (1-1)^2 = 0, which is the minimum possible value of f(A).

In the second test case, the sum of all elements in the grid is equal to 8, so the condition is satisfied. R_1 = 3, R_2 = 3, R_3 = 2 and C_1 = 3, C_2 = 2, C_3 = 3. Then, f(A) = (3-2)^2 + (3-2)^2 = 2. It can be proven, that it is the minimum possible value of f(A).

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
//import javafx.util.Pair;
import java.math.*;
import java.math.BigInteger;
import java.util.LinkedList; 
import java.util.Queue; 
public final  class CodeForces
{    
    static StringBuilder ans=new StringBuilder();
    static FastReader in=new FastReader();
    static ArrayList<ArrayList<Integer>> g;
    static long mod=998244353 ;
    static boolean set[];   
    //static Pair<Integer,Integer> seg[];
    //static int A[];
    public static void main(String args[])throws IOException
    {
        int T=i();
        while(T-->0)
        {
            int N=i();
            int K=i();
            int A[][]=new int[N][N];

            int e=K/N;
            int f[]=new int[N];
            Arrays.fill(f,e);
            e=K%N;
            for(int i=0; i<e; i++)f[i]++;
            // for(int i:f)System.out.print(i+" ");
            //System.out.println();
            for(int i=0; i<N; i++)
            {
                for(int j=0; j<f[i]; j++)
                {
                    int x=(j+i)%N;
                    // System.out.println(i+" "+j+" "+x);
                    A[x][i]=1;
                }
            }
            if(K%N==0)System.out.println(0);
            else System.out.println(2);
            for(int i=0; i<N; i++)
            {
                for(int j=0; j<N; j++)
                    System.out.print(A[i][j]);
                System.out.println();
            }
        }
    }

    static  long pow(long a,long b)
    {
        //long mod=1000000007;
        long pow=1;
        long x=a;
        while(b!=0)
        {
            if((b&1)!=0)pow=(pow*x)%mod;
            x=(x*x)%mod;
            b/=2;
        }
        return pow;
    }

    static void sort(long[] a) //check for long
    {
        ArrayList<Long> l=new ArrayList<>();
        for (long i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static String swap(String X,int i,int j)
    {
        char ch[]=X.toCharArray();
        char a=ch[i];
        ch[i]=ch[j];
        ch[j]=a;
        return new String(ch);
    }

    static int sD(long n)  
    {  

        if (n % 2 == 0 )  
            return 2;  

        for (int i = 3; i * i <= n; i += 2) {  
            if (n % i == 0 )  
                return i;  
        }  

        return (int)n;  
    }  

    static void setGraph(int N)
    {
        set=new boolean[N+1];
        g=new ArrayList<ArrayList<Integer>>();
        for(int i=0; i<=N; i++)
            g.add(new ArrayList<Integer>());
    }

    static void DFS(int N,int d)
    {
        set[N]=true;
        d++;
        for(int i=0; i<g.get(N).size(); i++)
        {
            int c=g.get(N).get(i);
            if(set[c]==false)
            {
                DFS(c,d);
            }
        }
    }

    static long toggleBits(long x)//one's complement || Toggle bits
    {
        int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

        return ((1<<n)-1)^x;
    }

    static int countBits(long a)
    {
        return (int)(Math.log(a)/Math.log(2)+1);
    }

    static long fact(long N)
    { 
        long n=2; 
        if(N<=1)return 1;
        else
        {
            for(int i=3; i<=N; i++)n=(n*i)%mod;
        }
        return n;
    }

    static int kadane(int A[])
    {
        int lsum=A[0],gsum=A[0];
        for(int i=1; i<A.length; i++)
        {
            lsum=Math.max(lsum+A[i],A[i]);
            gsum=Math.max(gsum,lsum);
        }
        return gsum;
    }

    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static boolean isPrime(long 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 int i()
    {
        return in.nextInt();
    }

    static long l()
    {
        return in.nextLong();
    }

    static int[] input(int N){
        int A[]=new int[N];
        for(int i=0; i<N; i++)
        {
            A[i]=in.nextInt();
        }
        return A;
    }

    static long[] inputLong(int N)     {
        long A[]=new long[N];
        for(int i=0; i<A.length; i++)A[i]=in.nextLong();
        return A;
    }

    static long GCD(long a,long b) 
    {
        if(b==0)
        {
            return a;
        }
        else return GCD(b,a%b );
    }

}
//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
class FastReader
{
    BufferedReader br;
    StringTokenizer st;
    public FastReader()
    {
        br=new BufferedReader(new InputStreamReader(System.in));
    }

    String next()
    {
        while(st==null || !st.hasMoreElements())
        {
            try
            {
                st=new StringTokenizer(br.readLine());
            }
            catch(IOException e)
            {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt()
    {
        return Integer.parseInt(next());
    }

    long nextLong()
    {
        return Long.parseLong(next());
    }

    double nextDouble()
    {
        return Double.parseDouble(next());
    }

    String nextLine()
    {
        String str="";
        try
        {
            str=br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }

}