How many strings can be obtained by applying the following operation on a string S exactly K times: "choose one lowercase English letter and insert it somewhere"?

The answer can be enormous, so print it modulo (10^9+7).

Constraints

• K is an integer between 1 and 10^6 (inclusive).
• S is a string of length between 1 and 10^6 (inclusive) consisting of lowercase English letters.

Input

Input is given from Standard Input in the following format:

K
S

Output

Print the number of strings satisfying the condition, modulo (10^9+7).

Examples

Input

5
oof

Output

575111451

Input

37564
whydidyoudesertme

Output

318008117

见题面

见题面