import sys
input = lambda :sys.stdin.readline()[:-1]
ni = lambda :int(input())
na = lambda :list(map(int,input().split()))
yes = lambda :print("yes");Yes = lambda :print("Yes");YES = lambda : print("YES")
no = lambda :print("no");No = lambda :print("No");NO = lambda : print("NO")
#######################################################################
"""

n が十分大きいとき

- k = 1 No
- k = 2 No
- k >= 3
#####
#



- 3 <= k <= n Yes

n = 5
####o
#ooo.
##o
#o
o


左下から2kマスで作る

"""


def solve(n, k):
    if k * 2 > n * n:
        return
    
    if k == 1:
        return
    if k == 2:
        if n == 2:
            return [[1, 1], [0, 0]]
        else:
            return
    if k <= n:
        res = [[0] * n for i in range(n)]
        for i in range(k-1):
            res[0][i] = 1
        res[1][0] = 1
        return res
    elif k == n * 2:
        res = [[0] * n for i in range(n)]
        for i in range(n):
            res[1][i] = 1
            res[2][i] = 1
        return res
    elif k == n * 2 + 1:
        res = [[0] * n for i in range(n)]
        for i in range(n):
            res[1][i] = 1
            res[2][i] = 1
        res[2][0] = 0
        res[3][0] = 1
        res[3][1] = 1
        return res
    else:
        res = [[0] * n for i in range(n)]
        cnt = k
        p, q = divmod(k * 2, n)
        if q == 0:
            p -= 1
            q = n
        # print(n, k, p, q)        
        for i in range(p):
            res[i][q-1] = 1
            cnt -= 1
        
        i = p - 1
        while i >= -1:
            if i == -1:
                i = 0
            for j in range(q-1):
                res[i][j] = 1
                cnt -= 1
            i -= 3

        i = p - 2
        while i >= -1:
            if i == -1:
                i = 0
            for j in range(q, n):
                res[i][j] = 1
                cnt -= 1
            i -= 3
        
        for i in range(n):
            for j in range(q-1, -1, -1):
                if res[i][j] == 0 and cnt > 0:
                    res[i][j] = 1
                    cnt -= 1
            for j in range(q, n):
                if res[i][j] == 0 and cnt > 0:
                    res[i][j] = 1
                    cnt -= 1

        return res
       
def check(n, k, res):
    A = 0
    B = 0
    for i in range(n):
        for j in range(n):
            A += res[i][j]
            if res[i][j] == 0:
                ok = 0
                for dx, dy in [[1, 0], [0, 1], [-1, 0], [0, -1]]:
                    x = i + dx
                    y = j + dy
                    if 0 <= x < n and 0 <= y < n and res[x][y]:
                        ok = 1
                B += ok
    # print(A, B)
    return A == B == k

# for n in range(1, 100):
#     for k in range(1, n * n):
#         res = solve(n, k)
#         if res is None:
#             continue
#         if not check(n, k, res):
#             print(n, k)
#             # for i in range(n):
#             #     print("".join([".#"[j] for j in res[i]]))
for _ in range(ni()):
    n, k = na()
    res = solve(n, k)
    
    if res is None:
        No()
    else:
        Yes()
        
        for i in range(n):
            print("".join([".#"[j] for j in res[i]]))
        assert check(n, k, res)