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
T = input()
P = input()

mod = 2 << 61-1
base = 1293

def gethash(S):
    H = 0
    b = 1
    for s in S[::-1]:
        H = (H + ord(s) * b) % mod
        b = b * base % mod
    return H

lp = len(P)
Hp = gethash(P)
Hs = gethash(T[:lp])
m = pow(base, lp, mod)

for i in range(len(T)-lp):
    if Hs == Hp:
        print(i)
    Hs = (Hs * base - ord(T[i]) * m + ord(T[i+lp])) % mod
if Hs == Hp:
    print(len(T)-lp)

