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B. DZY Loves Strings

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputDZY loves collecting special strings which only contain lowercase letters. For each lowercase letter *c* DZY knows its value *w*_{c}. For each special string *s* = *s*_{1}*s*_{2}... *s*_{|s|} (|*s*| is the length of the string) he represents its value with a function *f*(*s*), where

Now DZY has a string *s*. He wants to insert *k* lowercase letters into this string in order to get the largest possible value of the resulting string. Can you help him calculate the largest possible value he could get?

Input

The first line contains a single string *s* (1 ≤ |*s*| ≤ 10^{3}).

The second line contains a single integer *k* (0 ≤ *k* ≤ 10^{3}).

The third line contains twenty-six integers from *w*_{a} to *w*_{z}. Each such number is non-negative and doesn't exceed 1000.

Output

Print a single integer — the largest possible value of the resulting string DZY could get.

Examples

Input

abc

3

1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Output

41

Note

In the test sample DZY can obtain "abcbbc", *value* = 1·1 + 2·2 + 3·2 + 4·2 + 5·2 + 6·2 = 41.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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