This is an extension of ccc20j4. In this version constraints are higher. You can make hacks only if all versions of the problem are solved. Hacks are no longer being accepted.

Thuc likes finding cyclic shifts of strings. A cyclic shift of a string is obtained by moving characters from the beginning of the string to the end of the string. We also consider a string to be a cyclic shift of itself. For example, the cyclic shifts of ABCDE are:

ABCDE, BCDEA, CDEAB, DEABC, and EABCD.

Given some text, ~T~, and a string, ~S~, determine if ~T~ contains a cyclic shift of ~S~.

Input Specification

The input will consist of exactly two lines containing only uppercase letters. The first line will be the text ~T~, and the second line will be the string ~S~.

Subtask 1 [90%]

Each line will contain at most ~200\,000~ characters.

Subtask 2 [10%]

Each line will contain at most ~10^7~ characters.

Tip: the intended solution runs well within the time limit without constant optimization.

Output Specification

Output yes if the text, ~T~, contains a cyclic shift of the string, ~S~. Otherwise, output no.

Sample Input 1

ABCCDEABAA
ABCDE

Output for Sample Input 1

yes

Explanation of Output for Sample Input 1

CDEAB is a cyclic shift of ABCDE and is contained in the text ABC CDEAB AA.

Sample Input 2

ABCDDEBCAB
ABA

Output for Sample Input 2

no

Explanation of Output for Sample Input 2

The cyclic shifts of ABA are ABA, BAA, and AAB. None of these shifts are contained in the text ABCDDEBCAB.