#include <bits/stdc++.h>
inline bool EQ(double a, double b) { return fabs(a - b) < 1e-9; }
const int INF = 1 << 29;
inline int two(int n) { return 1 << n; }
inline int test(int n, int b) { return (n >> b) & 1; }
inline void set_bit(int &n, int b) { n |= two(b); }
inline void unset_bit(int &n, int b) { n &= ~two(b); }
inline int last_bit(int n) { return n & (-n); }
inline int ones(int n) {
  int res = 0;
  while (n && ++res) n -= n & (-n);
  return res;
}
template <class T>
void chmax(T &a, const T &b) {
  a = max(a, b);
}
template <class T>
void chmin(T &a, const T &b) {
  a = min(a, b);
}
long long gcd(long long a, long long b) {
  if (a == 0 || b == 0) return 0;
  if (a == b) return a;
  if (a > b) return gcd(a - b, b);
  return gcd(a, b - a);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long max(long long a, long long b) {
  if (a > b) return a;
  return b;
}
long long power(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = res * x;
    y = y >> 1;
    x = x * x;
  }
  return res;
}
long long powermod(long long x, long long y) {
  long long res = 1;
  x = x % 1000000007;
  while (y > 0) {
    if (y & 1) res = (res * x) % 1000000007;
    y = y >> 1;
    x = (x * x) % 1000000007;
  }
  return res;
}
long long mulmod(long long a, long long b) {
  long long res = 0;
  a %= 1000000007;
  while (b) {
    if (b & 1) res = (res + a) % 1000000007;
    a = (2 * a) % 1000000007;
    b >>= 1;
  }
  return res;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i += 6) {
    if ((n % i == 0) || (n % (i + 2) == 0)) return false;
  }
  return true;
}
long double dist(long long x1, long long y1, long long x2, long long y2) {
  return (long double)sqrt(
      (long double)((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)));
}
long long squaredist(long long x1, long long y1, long long x2, long long y2) {
  return ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
long long nCr(long long n, long long r) {
  if (r == 0) return 1;
  return (n * nCr(n - 1, r - 1)) / r;
}
long long countDivisors(long long n) {
  long long cnt = 0;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        cnt++;
      else
        cnt = cnt + 2;
    }
  }
  return cnt;
}
using namespace std;
int w[26];
bool comparator(char a, char b) { return w[a - 'a'] < w[b - 'a']; }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  int k;
  cin >> k;
  int maxi = INT_MIN;
  for (int i = 0; i < (26); i++) {
    cin >> w[i];
    maxi = max(maxi, w[i]);
  }
  long long int value = maxi * (k * (2 * s.length() + k + 1)) / 2;
  for (int i = 0; i < (s.length()); i++) {
    value += (i + 1) * w[s[i] - 'a'];
  }
  cout << value;
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

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 

<image>

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.

### Response

```cpp
#include <bits/stdc++.h>
inline bool EQ(double a, double b) { return fabs(a - b) < 1e-9; }
const int INF = 1 << 29;
inline int two(int n) { return 1 << n; }
inline int test(int n, int b) { return (n >> b) & 1; }
inline void set_bit(int &n, int b) { n |= two(b); }
inline void unset_bit(int &n, int b) { n &= ~two(b); }
inline int last_bit(int n) { return n & (-n); }
inline int ones(int n) {
  int res = 0;
  while (n && ++res) n -= n & (-n);
  return res;
}
template <class T>
void chmax(T &a, const T &b) {
  a = max(a, b);
}
template <class T>
void chmin(T &a, const T &b) {
  a = min(a, b);
}
long long gcd(long long a, long long b) {
  if (a == 0 || b == 0) return 0;
  if (a == b) return a;
  if (a > b) return gcd(a - b, b);
  return gcd(a, b - a);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long max(long long a, long long b) {
  if (a > b) return a;
  return b;
}
long long power(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = res * x;
    y = y >> 1;
    x = x * x;
  }
  return res;
}
long long powermod(long long x, long long y) {
  long long res = 1;
  x = x % 1000000007;
  while (y > 0) {
    if (y & 1) res = (res * x) % 1000000007;
    y = y >> 1;
    x = (x * x) % 1000000007;
  }
  return res;
}
long long mulmod(long long a, long long b) {
  long long res = 0;
  a %= 1000000007;
  while (b) {
    if (b & 1) res = (res + a) % 1000000007;
    a = (2 * a) % 1000000007;
    b >>= 1;
  }
  return res;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i += 6) {
    if ((n % i == 0) || (n % (i + 2) == 0)) return false;
  }
  return true;
}
long double dist(long long x1, long long y1, long long x2, long long y2) {
  return (long double)sqrt(
      (long double)((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)));
}
long long squaredist(long long x1, long long y1, long long x2, long long y2) {
  return ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
long long nCr(long long n, long long r) {
  if (r == 0) return 1;
  return (n * nCr(n - 1, r - 1)) / r;
}
long long countDivisors(long long n) {
  long long cnt = 0;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        cnt++;
      else
        cnt = cnt + 2;
    }
  }
  return cnt;
}
using namespace std;
int w[26];
bool comparator(char a, char b) { return w[a - 'a'] < w[b - 'a']; }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  int k;
  cin >> k;
  int maxi = INT_MIN;
  for (int i = 0; i < (26); i++) {
    cin >> w[i];
    maxi = max(maxi, w[i]);
  }
  long long int value = maxi * (k * (2 * s.length() + k + 1)) / 2;
  for (int i = 0; i < (s.length()); i++) {
    value += (i + 1) * w[s[i] - 'a'];
  }
  cout << value;
  return 0;
}

```