#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=5e3+5,M=N*4+5,K=1000+5,mod=1e9+7,Mod=mod-1;const db eps=1e-9;const int INF=1e9+7;mt19937 rnd(28382);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;
int n,m,d[N],e[N][N];
void Solve(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++) for(int j=i+1;j<=n;j++) e[i][j]=0;
	for(int i=1;i<=n;i++) d[i]=i-1;
	for(int i=n-1;i*2>n&&m;i--){
		for(int j=i+1;j<=n&&m;j++){
			if(m>=i-(n-1-i)-1) m-=i-(n-1-i)-1,d[j]--,d[n-j+1]++;
			else d[j]--,d[i+1-m-1]++,m=0;
		}
	}
	if(m){puts("No");return;}puts("Yes");
	for(int i=1;i<=n;i++) gdb(d[i]);
	for(int i=n;i;i--){
		d[i]=i-d[i]-1;
		for(int r=i-1,l;r;r=l-1){
			for(l=r;d[l]==d[r]&&l;l--);l++;
			for(int j=l;j<=r&&d[i];j++) e[j][i]=1,d[i]--,d[j]--;
		}
		gdb(d[1],d[2]);
	}
	for(int i=2;i<=n;putchar('\n'),i++) for(int j=1;j<i;j++) putchar('0'^e[j][i]^1);
}
int main(){
	int t=1;
	scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}