#include <bits/stdc++.h>

#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using u32 = unsigned int;
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

template<class T>inline void chkmn(T &x, T y) { if (y < x) x = y; }
template<class T>inline void chkmx(T &x, T y) { if (y > x) x = y; }

using namespace std;

const int maxn = 1010;
const int maxm = 80010;

int n, m, k, q, b[maxn], p[maxn], pmn[maxn], len[maxm][32], fp[maxm], ps[maxm];
int sta[maxm][32], mi[maxm], tot, a[32], to0[maxm], precnt, to1[maxm][32], W[maxm][32];
u32 coe0[maxm], f[maxm], g[maxm], self[maxm];
map<vector<int>, int> mp;
string s;

void dfs(int dep, int sum) {
  if (dep == k + 1) {
    a[k]++;
    a[0] = 0;
    mi[++tot] = sum;
    rep (i, 0, k) sta[tot][i] = a[i];
    vector<int> p(k + 1);
    rep (i, 0, k) p[i] = a[i];
    mp[p] = tot;
    a[0] = 1;
    mi[++tot] = sum;
    rep (i, 0, k) sta[tot][i] = a[i];
    rep (i, 0, k) p[i] = a[i];
    mp[p] = tot;
    a[k]--;
    return;
  }
  rep (x, 0, (31 - sum) / dep) a[dep] = x, dfs(dep + 1, sum + x * dep);
}

u32 solve() {
  u32 ans = 0;
  rep (_, 1, tot) {
    int ok = 1;
    u32 val = f[_];
    rep (i, 0, k - 1) {
      if (!val) break;
      if (m >> i & 1) {
        if (sta[_][i] == 0) {
          val *= (precnt - len[_][i] + 1);
        }
      } else {
        if (sta[_][i] > 0) ok = 0;
      }
    }
    if (ok) ans += val;
  }
  return ans;
}

int main() {
  cin.tie(nullptr) -> ios::sync_with_stdio(false);
  cin >> n >> k >> q >> s, b[1] = 1;
  rep (i, 2, n) b[i] = (s[i - 2] == 'A' ? 1 : 0);
  dfs(1, 0);
  rep (_, 1, tot) {
    vector<int> p(k + 1);
    rep (i, 0, k) p[i] = sta[_][i];
    int pos = 0;
    while (pos < k && !p[pos]) pos++;
    if (pos) p[pos]++;
    to0[_] = mp[p], coe0[_] = 1u << pos;
  }
  int s = 0;
  rep (_, 1, tot) {
    vector<int> p(k + 1);
    rep (i, 0, k) p[i] = sta[_][i];
    per (i, k, 0) len[_][i] += len[_][i + 1] + max(0, p[i] - 1);
    while (fp[_] <= k && !p[fp[_]]) fp[_]++;
    rep (w, -1, k - 1) if (mi[_] + (w == -1 ? k : w) < 32) {
      s++;
      if (w == -1) {
        self[_] += (1u << k);
      } else {
        if (p[w] > 0) {
          self[_] -= (1u << w);
        } else {
          p[w] = 1;
          W[_][ps[_]] = w, to1[_][ps[_]++] = mp[p];
          p[w] = 0;
        }
      }
    }
  }
  vector<int> p(k + 1, 0);
  p[k] = 1, f[mp[p]] = 1;
  rep (i, 1, n) {
    rep (j, 1, tot) g[j] = f[j], f[j] = 0;
    if (b[i] == 0) {
      precnt++;
      rep (j, 1, tot) f[to0[j]] += g[j] * coe0[j];
    } else {
      int cnt = 0;
      rep (j, 1, tot) if (g[j]) {
        f[j] += g[j] * self[j];
        rep (id, 0, ps[j] - 1) {
          cnt++;
          int w = W[j][id], tar = to1[j][id];
          if (w < fp[j]) {
            f[tar] -= g[j] << w;
          } else {
            f[tar] -= (g[j] * (precnt - len[j][w] + 1)) << w;
          }
        }
      }
    }
  }
  while (q--) {
    cin >> m;
    cout << solve() << '\n';
  }
}