You know that the Martians use a number system with base k . Digit b ( 0 ≤ b < k ) is considered lucky , as the first contact between the Martians and the Earthlings occurred in year b (by Martian chronology). A digital root d ( x ) of number x is a number that consists of a single digit, resulting after cascading summing of all digits of number x . Word "cascading" means that if the first summing gives us a number that consists of several digits, then we sum up all digits again, and again, until we get a one digit number. For example, d (3504 7 ) = d ((3 + 5 + 0 + 4) 7 ) = d (15 7 ) = d ((1 + 5) 7 ) = d (6 7 ) = 6 7 . In this sample the calculations are performed in the 7-base notation. If a number's digital root equals b , the Martians also call this number lucky. You have string s , which consists of n digits in the k -base notation system. Your task is to find, how many distinct substrings of the given string are lucky numbers. Leading zeroes are permitted in the numbers. Note that substring s i ... j of the string s = a 1 a 2 ... a n ( 1 ≤ i ≤ j ≤ n ) is the string a i a i + 1 ... a j . Two substrings s i 1 ... j 1 and s i 2 ... j 2 of the string s are different if either i 1 ≠ i 2 or j 1 ≠ j 2 . The first line contains three integers k , b and n ( 2 ≤ k ≤ 10 9 , 0 ≤ b < k , 1 ≤ n ≤ 10 5 ). The second line contains string s as a sequence of n integers, representing digits in the k -base notation: the i -th integer equals a i ( 0 ≤ a i < k ) — the i -th digit of string s . The numbers in the lines are space-separated. Print a single integer — the number of substrings that are lucky numbers. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. In the first sample the following substrings have the sought digital root: s 1... 2 = "3 2", s 1... 3 = "3 2 0", s 3... 4 = "0 5", s 4... 4 = "5" and s 2... 6 = "2 0 5 6 1".