#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
int edge[5007][5007];
ll deg[5007];
void solve()
{
ll n,m;
cin >> n >> m;
ll W = (n*(n-1)*(n-2))/6-m;
ll S = 2*W+n*(n-1)/2;
ll min_sum = 0;
if(n%2 == 1) min_sum = n*((n-1)/2)*((n-1)/2);
else min_sum = (n/2)*(((n-2)/2)*((n-2)/2)+(n/2)*(n/2));
if(S%2 != min_sum%2 || S < min_sum)
{
cout << "No\n";
return;
}
rep3(i,2,n,2)
{
rep2(j,1,(i-1)/2)
{
edge[i][j] = 1;
edge[j][i] = 0;
edge[i+1][j] = 0;
edge[j][i+1] = 1;
}
rep2(j,(i-1)/2+1,i-1)
{
edge[i][j] = 0;
edge[j][i] = 1;
edge[i+1][j] = 1;
edge[j][i+1] = 0;
}
edge[i][i+1] = 1;
edge[i+1][i] = 0;
}
if(n%2 == 0)
{
rep2(i,1,n/2)
{
edge[n][i] = 1;
edge[i][n] = 0;
}
rep2(i,n/2+1,n-1)
{
edge[n][i] = 0;
edge[i][n] = 1;
}
}
rep2(i,1,n) edge[i][i] = 0;
rep2(i,1,n)
{
deg[i] = 0;
rep2(j,1,n) deg[i] += edge[i][j];
}
while(true)
{
rep2(i,1,n)
{
rep2(j,1,n)
{
if(i == j || deg[j] == 0 || deg[i] < deg[j] || edge[i][j] || min_sum+2*(deg[i]-deg[j]+1) > S) continue;
edge[i][j] ^= 1;
edge[j][i] ^= 1;
min_sum += 2*(deg[i]-deg[j]+1);
deg[i]++;
deg[j]--;
}
}
if(min_sum == S) break;
}
cout << "Yes\n";
rep2(i,2,n)
{
rep2(j,1,i-1)
{
cout << edge[i][j];
}
cout << "\n";
}
}
int main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
//random_start();
int t = 1;
cin >> t;
while(t--) solve();
}
