#include <iostream>

typedef long long ll;
typedef double lf;

// #define DEBUG 1
struct IO
{
    #define MAXSIZE (1 << 20)
    #define isdigit(x) (x >= '0' && x <= '9')
    char buf[MAXSIZE], *p1, *p2;
    char pbuf[MAXSIZE], *pp;
    #if DEBUG
    #else
    IO() : p1(buf), p2(buf), pp(pbuf) {}
    ~IO() {fwrite(pbuf, 1, pp - pbuf, stdout);}
    #endif
    #define gc() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, MAXSIZE, stdin), p1 == p2) ? ' ' : *p1++)
    #define blank(x) (x == ' ' || x == '\n' || x == '\r' || x == '\t')

    template <typename T>
    void Read(T &x)
    {
        #if DEBUG
        std::cin >> x;
        #else
        bool sign = 0; char ch = gc(); x = 0;
        for (; !isdigit(ch); ch = gc())
            if (ch == '-') sign = 1;
        for (; isdigit(ch); ch = gc()) x = x * 10 + (ch ^ 48);
        if (sign) x = -x;
        #endif
    }
    void Read(char *s)
    {
        #if DEBUG
        std::cin >> s;
        #else
        char ch = gc();
        for (; blank(ch); ch = gc());
        for (; !blank(ch); ch = gc()) *s++ = ch;
        *s = 0;
        #endif
    }
    void Read(char &c) {for (c = gc(); blank(c); c = gc());}

    void Push(const char &c)
    {
        #if DEBUG
        putchar(c);
        #else
        if (pp - pbuf == MAXSIZE) fwrite(pbuf, 1, MAXSIZE, stdout), pp = pbuf;
        *pp++ = c;
        #endif
    }
    template <typename T>
    void Write(T x)
    {
        if (x < 0) x = -x, Push('-');
        static T sta[35];
        int top = 0;
        do sta[top++] = x % 10, x /= 10; while (x);
        while (top) Push(sta[--top] ^ 48);
    }
    template <typename T>
    void Write(T x, char lst) {Write(x), Push(lst);}
} IO;
#define Read(x) IO.Read(x)
#define Write(x, y) IO.Write(x, y)
#define Put(x) IO.Push(x)

using namespace std;

const int MAXN = 5010;

int n; ll m;
ll d[MAXN];
bool e[MAXN][MAXN];

inline int Calc()
{
    int cnt = 0;
    for (int i = 1; i <= n; i++)
        for (int j = i + 1; j <= n; j++)
            for (int k = j + 1; k <= n; k++)
                if ((e[i][j] && e[j][k] && !e[i][k]) || (!e[i][j] && !e[j][k] && e[i][k]))
                    cnt++;
    return cnt;
}

int st[MAXN], top;

int main()
{
    // freopen("C.in", "r", stdin);
    // freopen("C.out", "w", stdout);
    #if DEBUG
    #else
    ios::sync_with_stdio(0), cin.tie(0);
    #endif
    // for (int i = 3; i <= 9; i++)
    //     for (int j = 0; j <= i * i / 3; j++)
    //         cout << i << ' ' << j << '\n';
    // return 0;
    int T;
    Read(T);
    while (T--)
    {
        Read(n), Read(m);
        ll sum = (ll)n * (n - 1) * (n - 2) / 3 + (ll)n * (n - 1) / 2 - 2 * m;
        if (n & 1)
            for (int i = 1; i <= n; i++) d[i] = n >> 1;
        else
        {
            for (int i = 1; i <= n >> 1; i++) d[i] = (n >> 1) - 1;
            for (int i = (n >> 1) + 1; i <= n; i++) d[i] = n >> 1;
        }
        ll cur = 0;
        for (int i = 1; i <= n; i++) cur += d[i] * d[i];
        // for (int i = 1; i <= n; i++) cout << d[i] << ' '; cout << '\n';
        // cout << cur << ' ' << sum << '\n';
        if (sum < cur) { cout << "No\n"; continue; }
        for (int i = 1; i <= n / 2; i++)
            while (d[i] > i - 1 && cur + 2 * (d[n - i + 1] - d[i]) + 2 <= sum) cur += 2 * (d[n - i + 1] - d[i]) + 2, d[i]--, d[n - i + 1]++;
        if (cur == sum - 2)
        {
            d[n + 1] = -1;
            for (int i = 1; i < n; i++)
                if (d[i] > i - 1 && d[i] == d[i + 1] && d[i + 1] != d[i + 2])
                { d[i]--, d[i + 1]++, cur += 2; break; }
        }
        // for (int i = 1; i <= n; i++) cout << d[i] << ' '; cout << '\n';
        // cout << cur << ' ' << sum << '\n';
        if (cur != sum) cout << "Error " << n << ' ' << m << '\n';
        for (int i = 1; i < n; i++)
        {
            top = 0;
            for (int l = i + 1, r; l <= n; l = r + 1)
            {
                r = l;
                while (r < n && d[r + 1] == d[l]) r++;
                for (int k = r; k >= l; k--) st[++top] = k;
            }
            for (int j = 1; j <= d[i]; j++) e[i][st[j]] = 1;
            for (int j = d[i] + 1; j <= top; j++) e[i][st[j]] = 0, d[st[j]]--;
        }
        // for (int i = 1; i <= n; i++) cout << d[i] << ' '; cout << '\n';
        cout << "Yes\n";
        for (int i = 2; i <= n; i++, cout << '\n')
            for (int j = 1; j < i; j++)
                cout << e[j][i];
        // int cnt = Calc();
        // if (cnt != m) cout << "WA " << n << ' ' << m << ' ' << cnt << "\n";
    }
    return 0;
}