import numpy as np

def solution(m):
    stable_ores, unstable_ores = categorize_ores(m)

    if 0 in stable_ores:
        return [1]+[0]*(len(stable_ores)-1)+[1]

    p = np.array(m)
    q = np.zeros(p.shape, dtype=int)
    for i in range(len(m)):
        q[i][i] = sum(p[i])
    r = q - p

    t = gaussian_elimination(r, stable_ores, unstable_ores)

    numerators = -t[0][stable_ores]
    denominator = sum(numerators)

    result = np.hstack((numerators, denominator))
    g = abs_gcd(*list(result))

    return list(result / g)

def categorize_ores(m):
    stable_ores = []
    unstable_ores = []
    for i in range(len(m)):
        if sum(m[i]) == 0:
            stable_ores += [i]
        else:
            unstable_ores += [i]
    return stable_ores, unstable_ores

def gaussian_elimination(r, s, u):
    arr = r
    for i in range(len(u)):
        for j in range(i+1, len(u)):
            row_up, row_down = arr[u[i]], arr[u[j]]
            if row_down[u[i]] != 0:
                arr[u[j]] = row_down*arr[u[i]][u[i]] - row_up*arr[u[j]][u[i]]
                arr[u[j]] = arr[u[j]] / abs_gcd(*list(arr[u[j]]))
    for i in reversed(range(len(u))):
        for j in reversed(range(i)):
            row_down, row_up = arr[u[i]], arr[u[j]]
            if row_up[u[i]] != 0:
                arr[u[j]] = row_up*row_down[u[i]] - row_down*row_up[u[i]]
                arr[u[j]] = arr[u[j]] / abs_gcd(*list(arr[u[j]]))
    return arr

def abs_gcd(*args):
    if len(args) == 1:
        return abs(args[0])
    if len(args) == 2:
        m, n = abs(args[0]), abs(args[1])
        while n != 0:
            t = m % n
            m, n = n, t
        return abs(m)
    return abs_gcd(args[0], abs_gcd(*args[1:]))

tests = [
        [
            [[0, 2, 1, 0, 0], [0, 0, 0, 3, 4], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]],
            [7, 6, 8, 21]
        ],
        [
            [[0, 1, 0, 0, 0, 1], [4, 0, 0, 3, 2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]],
            [0, 3, 2, 9, 14]
        ],
        [
            [[0, 1, 0, 0, 0, 1], [4, 0, 0, 3, 2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0]],
            [0, 3, 11, 14]
        ],
        [
            [[0, 1, 0, 0, 0, 1], [4, 0, 0, 3, 2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]],
            [0, 1, 6, 7]
        ],
        [
            [[0]],
            [1, 1]
        ],
        [
            [[0, 1], [0, 0]],
            [1, 1]
        ],
        [
            [[0, 5, 0, 3], [0, 0, 4, 1], [0, 0, 0, 0], [0, 0, 0, 0]],
            [1, 1, 2]
        ],
]

#print(solution(tests[1][0]), tests[1][1])

for test in tests:
    result = solution(test[0])
    print(result == test[1], result, test[1])