Mancunian is stuck in biology class again! This time, the class is learning about the DNA of googlibodies.
Googlibodies are a rare breed of chameleons found on Red Island and visible only to the most devout Manchester United supporters. Being rare, their genes are also special. Instead of the normal A,T,G,C, they can contain any of 26 possible nucleotides, each represented by a lowercase Latin letter.
Each student is given the DNA sequence of a googlibody, of length L. Genes are found as substrings in that sequence. A fantabulous gene is one that reads the same forwards and backwards. The value of a gene is defined as the product of the length of the gene with the number of distinct nucleotides present in it.
Given a parameter K, Mancunian has to find out the number of distinct fantabulous genes having value not less than K.
Input format
The first line contains two integers L and K, denoting the length of the DNA sequence and the specified parameter respectively.
The second line contains the sequence of length L, each character of which is a lowercase Latin letter, lying between a to z.
Output format
Print a single integer, which is the the number of fantabulous genes having a value not less than K.
Constraints
- 1≤L≤100,000
- 1≤K≤1,000,000,000
There are 9 distinct fantabulous genes a, b, c, d, y, z, ada, bcb and abcba, having values 1, 1, 1, 1, 1, 1, 6, 6, and 15 respectively.
