This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<iostream>
#include<vector>
using namespace std;
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int t;
int n, m;
cin >> t;
while(t--){
cin >> n >> m;
if(m <= n - 2){
cout << "Yes\n";
for(int i = 2; i < n; i++) {
for(int j = 1; j < i; j++) cout << "1";
cout << "\n";
}
for(int j = 1; j < n; j++){
if(j + m == n - 1) cout << "0";
else cout << "1";
}
cout << "\n";
continue;
}
else if(n <= 7){
int tot = n * (n - 1) / 2;
int ans = -1, cnt;
vector<vector<int>> edges(n + 1, vector<int>(n + 1));
for(int i = 0; i < (1 << tot); i++){
cnt = 0;
for(int j = 2; j <= n; j++){
for(int k = 1; k < j; k++){
if((1 << cnt) & i){
edges[k][j] = 1;
}
else edges[k][j] = 0;
cnt++;
}
}
cnt = 0;
for(int j = 1; j <= n; j++){
for(int k = j + 1; k <= n; k++){
for(int l = k + 1; l <= n; l++){
if(edges[j][k] == edges[k][l] && edges[j][k] != edges[j][l]) cnt++;
}
}
}
if(cnt == m){
ans = i;
break;
}
}
if(ans == -1) cout << "No\n";
else{
cout << "Yes\n";
cnt = 0;
for(int i = 2; i <= n; i++){
for(int j = 1; j < i; j++){
if(ans & (1 << cnt)) cout << "1";
else cout << "0";
cnt++;
}
cout << "\n";
}
}
continue;
}
}
}
// g++ -std=c++17 -Wall -Wextra -Wshadow -fsanitize=undefined -fsanitize=address -o run pingpong.cpp
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