Vasya plays the LionAge II. He was bored of playing with a stupid computer, so he installed this popular MMORPG, to fight with his friends. Vasya came up with the name of his character — non-empty string s, consisting of a lowercase Latin letters. However, in order not to put up a front of friends, Vasya has decided to change no more than k letters of the character name so that the new name sounded as good as possible. Euphony of the line is defined as follows: for each pair of adjacent letters x and y (x immediately precedes y) the bonus c(x, y) is added to the result. Your task is to determine what the greatest Euphony can be obtained by changing at most k letters in the name of the Vasya's character.

Input

The first line contains character's name s and an integer number k (0 ≤ k ≤ 100). The length of the nonempty string s does not exceed 100. The second line contains an integer number n (0 ≤ n ≤ 676) — amount of pairs of letters, giving bonus to the euphony. The next n lines contain description of these pairs «x y c», which means that sequence xy gives bonus c (x, y — lowercase Latin letters,  - 1000 ≤ c ≤ 1000). It is guaranteed that no pair x y mentioned twice in the input data.

Output

Output the only number — maximum possible euphony оf the new character's name.

Examples

Input

winner 4
4
s e 7
o s 8
l o 13
o o 8


Output

36

Input

abcdef 1
5
a b -10
b c 5
c d 5
d e 5
e f 5


Output

20

Note

In the first example the most euphony name will be looser. It is easy to calculate that its euphony is 36.
#include <bits/stdc++.h>
using namespace std;
const int MAX_N = 100 + 10;
const int MAX_CH = 130;
const int INF = (1 << 30);
int N, K;
string S;
int D[MAX_N][MAX_N][MAX_CH];
int W[MAX_CH][MAX_CH];
int Ans = -INF - 1;
void init() {
  for (int i = 0; i < MAX_N; i++)
    for (int j = 0; j < MAX_N; j++)
      for (int k = 0; k < MAX_CH; k++) D[i][j][k] = -INF;
  D[0][0][(int)'z' + 1] = 0;
}
int main() {
  ios::sync_with_stdio(false);
  cin >> S >> K;
  cin >> N;
  for (int i = 0; i < N; i++) {
    char a, b;
    int c;
    cin >> a >> b >> c;
    W[(int)a][(int)b] = c;
  }
  init();
  for (int i = 1; i <= (int)S.size(); i++)
    for (int j = 0; j <= i && j <= K; j++)
      for (int now = (int)'a'; now <= (int)'z'; now++)
        for (int prev = (int)'a'; prev <= (int)'z' + 1; prev++) {
          if (now == S[i - 1]) {
            D[i][j][now] = max(D[i - 1][j][prev] + W[prev][now], D[i][j][now]);
          } else if (j != 0) {
            D[i][j][now] =
                max(D[i - 1][j - 1][prev] + W[prev][now], D[i][j][now]);
          }
        }
  for (int i = 0; i <= K; i++)
    for (int ch = (int)'a'; ch <= (int)'z'; ch++)
      Ans = max(Ans, D[(int)S.size()][i][ch]);
  cout << Ans << endl;
  return 0;
}
