beecrowd | 2001

# Bile

By Alisson Soares, UECE Brazil

Timelimit: 5

Bile is a smart kid who likes quite recurrences. He was participating in a competition in which the best sequence wins a prize. Bile created a sequence F, in the sequence, the first N values are known, and to discover the value of Fk for a K N is used to formulate below.

For N K: FK = 1*FK-1 + 2*FK-2 + ... + N*FK-N

But he does not know calculate quickly the values of their sequence and asked for your help.

In the first test case: N = 2, K = 3, F1 = 2, F2 = 5, F3 = F2 + 2*F1 = 9, F4 = F3 + 2*F2 = 19 ...

## Input

The input consists of several test cases. Each test case consists of two lines. The first line of each test case contains two integers, N ( 2 ≤ N ≤ 100 ) and K ( NK ≤ 1018 ), representing the number of values of the first known sequence Bile. The second line consists of N integers Fi ( F1, F2, … ,FN ) and ( 0 ≤ Fi ≤ 1010 ) representing the values initially known. The entry ends with the final file (EOF).

## Output

For each test case you should to print the value FK and the sum of all elements of bile function minor or equal to FK, separated by a single space. Your answers should be submitted in module 303700049.

 Input Sample Output Sample 2 3 2 5 5 6 1 2 3 4 5 9 16 35 50