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 kmpTable(w):
    lw = len(w)
    nx = [-1] * (lw + 1)
    j = -1
    for i in range(lw):
        while j >= 0 and w[i] != w[j]:
            j = nx[j]
        j += 1
        nx[i + 1] = j
    return nx
def kmpSearch(s, w):
    ls = len(s)
    start = 0
    w_idx = 0
    ret = []
    nx = kmpTable(w)
    while start + w_idx < ls:
        if s[start + w_idx] == w[w_idx]:
            w_idx += 1
            if w_idx == len(w):
                ret.append(start)
                start = start + w_idx - nx[w_idx]
                w_idx = nx[w_idx]
        else:
            if w_idx == 0:
                start += 1
            else:
                start = start + w_idx - nx[w_idx]
                w_idx = nx[w_idx]
    return ret
T = input()
P = input()
ans = kmpSearch(T, P)
for i in ans:
    print(i)

