Find places where a string P is found within a text T. Print all indices of T where P found. The indices of T start with 0.

Constraints

* 1 ≤ length of T ≤ 1000000
* 1 ≤ length of P ≤ 10000
* The input consists of alphabetical characters and digits

Input

In the first line, a text T is given. In the second line, a string P is given.

Output

Print an index of T where P found in a line. Print the indices in ascending order.

Examples

Input

aabaaa
aa


Output

0
3
4


Input

xyzz
yz


Output

1


Input

abc
xyz


Output
def make_kmp_table(t):
    i = 2
    j = 0
    m = len(t)
    tbl = [0] * (m + 1)
    tbl[0] = -1
    while i <= m:
        if t[i - 1] == t[j]:
            tbl[i] = j + 1
            i += 1
            j += 1
        elif j > 0:
            j = tbl[j]
        else:
            tbl[i] = 0
            i += 1
    return tbl


def kmp(s, t):
    matched_indices = []
    tbl = make_kmp_table(t)
    i = 0
    j = 0
    n = len(s)
    m = len(t)
    while i + j < n:
        if t[j] == s[i + j]:
            j += 1
            if j == m:
                matched_indices.append(i)
                i += j - tbl[j]
                j = tbl[j]
        else:
            i += j - tbl[j]
            if j > 0:
                j = tbl[j]
    return matched_indices


t = input()
p = input()
result = kmp(t, p)
if result:
    print(*result, sep='\n')
