String Search

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

inputFormat

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.

outputFormat

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

样例

xyzz
yz

1