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
#!/usr/bin/python
B=999999937
P=1000000007

def gen_hash(s,hash):
	c=0
	for i in range(len(s)):
		c=(c*B+s[i])%P
		hash[i]=c

import sys
s=[ord(e) for e in sys.stdin.readline().strip()]
ls=len(s)
v=[0]*ls
hsh=[0]*10001
gen_hash(s,v)
q=[ord(e) for e in sys.stdin.readline().strip()]
lq=len(q)
gen_hash(q,hsh)
hash=hsh[lq-1]
Brev=pow(B,lq,P)
r=[]
for i in range(lq-1,ls):
	if v[i]==((v[i-lq] if i>=lq else 0)*Brev+hash)%P:
		r.append(i-lq+1)
for e in r:print(e)