Alphabet Ak consists of k initial letters of English alphabet. A positive integer called a weight is assigned to each letter of the alphabet. A weight of a word built from the letters of the alphabet Ak is the sum of weights of all letters in this word. A language over an alphabet Ak is any finite set of words built from the letters of this alphabet. A weight of a language is the sum of weights of all its words. We say that the language is prefixless if for each pair of different words w, v from this language w is not a prefix of v.
We want to find out what is the minimal possible weight of an n-element, prefixless language over an alphabet Ak.
Example
Assume that k = 2 , the weight of the letter a - W(a)=2 and the weight of the letter b - W(b) = 5. The weight of the word ab - W(ab)= 2+5=7. W(aba)=2+5+2=9. The weight of the language J = {ab, aba, b} - W(J) = 21. The language J is not prefixless, since the word ab is a prefix of aba. The lightest tree-element, prefixless language over the alphabet A2 (assuming that weights of the letters are as before) is {b, aa, ab}; its weight is 16.
Task
Write a program that:
1.reads two integers n, k and the weights of k letters of an alphabet Ak;
2.computes the minimal weight of a prefixless, n-element language over the alphabet Ak;