beecrowd | 2001
# Bile

**Timelimit: 5**

By Alisson Soares, UECE Brazil

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 *F*_{k} for a *K* *N* is used to formulate below.

For* N* *K*: *F*_{K} = 1**F*_{K-1} + 2**F*_{K-2} + ... + *N***F*_{K-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, *F*_{1} = 2, *F*_{2} = 5, *F*_{3} = *F*_{2} + 2**F*_{1} = 9, *F*_{4 }= *F*_{3} + 2**F*_{2} = 19 ...

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** ( **N** ≤ **K** ≤ 10^{18} ), representing the number of values of the first known sequence Bile. The second line consists of **N** integers **F**_{i} ( **F**_{1}, **F**_{2}, … ,**F**_{N} ) and ( 0 ≤ **F**_{i} ≤ 10^{10} ) representing the values initially known. The entry ends with the final file (EOF).

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

Input Sample | Output Sample |

2 3 |
9 16 |