"""Z-algorithm: linear-time Z-array and substring search.

Z[i] = length of the longest substring of s starting at i that is also a
prefix of s.  Z[0] is conventionally len(s) (or 0, depending on source);
here Z[0] = len(s) for convenience, matching the common competitive-programming
convention.

Complexity: O(n) time, O(n) space.
"""


def z_function(s: str):
    """Return the Z-array of s."""
    n = len(s)
    z = [0] * n
    if n == 0:
        return z
    z[0] = n
    l = r = 0
    for i in range(1, n):
        if i < r:
            z[i] = min(r - i, z[i - l])
        while i + z[i] < n and s[z[i]] == s[i + z[i]]:
            z[i] += 1
        if i + z[i] > r:
            l, r = i, i + z[i]
    return z


def search(pattern: str, text: str):
    """Return list of starting indices in text where pattern occurs (possibly overlapping)."""
    if pattern == "":
        return list(range(len(text) + 1))
    if len(pattern) > len(text):
        return []
    combined = pattern + "\x00" + text
    z = z_function(combined)
    m = len(pattern)
    res = []
    offset = m + 1
    for i in range(offset, len(combined)):
        if z[i] >= m:
            res.append(i - offset)
    return res


def _self_test():
    assert z_function("") == []
    assert z_function("a") == [1]
    assert z_function("aaaa") == [4, 3, 2, 1]
    assert z_function("ababa") == [5, 0, 3, 0, 1]
    assert search("ab", "abxab") == [0, 3]
    assert search("aa", "aaaa") == [0, 1, 2]
    assert search("", "abc") == [0, 1, 2, 3]
    assert search("xyz", "abc") == []
    print("OK z_algorithm self-test")


if __name__ == "__main__":
    _self_test()
    import sys
    if len(sys.argv) > 1:
        print(z_function(sys.argv[1]))