human
Give me a Python code to print a single integer — the largest possible value of the resulting string DZY could get given the following:
DZY loves collecting special strings which only contain lowercase letters. For each lowercase letter c DZY knows its value wc. For each special string s = s1s2... 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| ≤ 103).

The second line contains a single integer k (0 ≤ k ≤ 103).

The third line contains twenty-six integers from wa to wz. 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.
from
assistant
#Here is Python code to print a single integer — the largest possible value of the resulting string DZY could get.
collections import deque, Counter, OrderedDict
from heapq import nsmallest, nlargest
from math import ceil,floor,log,log2,sqrt,gcd,factorial,pow,pi

def binNumber(n,size=4):
    return bin(n)[2:].zfill(size)

def iar():
    return list(map(int,input().split()))

def ini():
    return int(input())

def isp():
    return map(int,input().split())

def sti():
    return str(input())

def par(a):
    print(' '.join(list(map(str,a))))

def tdl(outerListSize,innerListSize,defaultValue = 0):
    return [[defaultValue]*innerListSize for i in range(outerListSize)]

def sts(s):
    s = list(s)
    s.sort()
    return ''.join(s)

class pair:
    def __init__(self,f,s):
        self.fi = f
        self.se = s
    def __lt__(self,other):
        return (self.fi,self.se) < (other.fi,other.se)

#  =========     /\       /|    |====/|
#      |        /  \       |    |   / |
#      |       /____\      |    |  /  |
#      |      /      \     |    | /   |
#  ========= /        \  =====  |/====|  
#  code

if __name__ == "__main__":
    s = sti()
    n = ini()
    a = iar()
    cnt = 0
    v = max(a)
    for i in range(len(s)):
        cnt += ( a[ord(s[i])-97] * (i+1) )
    c = len(s) + 1
    while n > 0:
        cnt += v*c
        c += 1
        n -= 1
    print(cnt)