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
import queue
T = str(input())
NN = len(T)
T2 = [0] * NN
P = str(input())
N = len(P)
P2 = [0] * N

alpha2num = lambda c: ord(c) - ord('0') + 1
#print(alpha2num("1"))
#print(alpha2num("A"))
#print(alpha2num("a"))
for i in range(N):
  P2[i] = alpha2num(P[i])
#print(P2)
for i in range(NN):
  T2[i] = alpha2num(T[i])
#print(T2)

for i in range(NN - N + 1):
  if T[i:i + N] == P:
    print(i)



