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 atoi(a):
    return ord(a) + (1 << 31)


S = input()
T = input()
ns = len(S)
nt = len(T)

if ns < nt:
    exit()

mod = (1 << 61) - 1
b = 10 ** 9 + 7
bn = pow(b, nt, mod)

hs = 0
ht = 0

for s, t in zip(S, T):
    hs = (hs * b + atoi(s)) % mod
    ht = (ht * b + atoi(t)) % mod

for i in range(ns - nt + 1):
    if hs == ht:
        print(i)
    if ns - nt <= i:
        break
    hs = (hs * b + atoi(S[i + nt]) - bn * atoi(S[i])) % mod
