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| #include <cstdio> using namespace std; template <class Type> void read (Type &x) { char c; bool flag = false; while ((c = getchar()) < '0' || c > '9') flag |= c == '-'; x = c - '0'; while ((c = getchar()) >= '0' && c <= '9') x = (x << 3) + (x << 1) + c - '0'; if (flag) x = ~x + 1; } template <class Type, class ...Rest> void read (Type &x, Rest &...y) { read(x); read(y...); } template <class Type> void write (Type x) { if (x < 0) putchar('-'), x = ~x + 1; if (x > 9) write(x / 10); putchar('0' + x % 10); } typedef long long LL; const int N = 510, mod = 1e9 + 7; char s[N]; int n, m; void adj (int &x) { x += x >> 31 & mod; } struct ModInt { int x; ModInt (int _ = 0) { adj(x = _); } int operator () () const { return x; } ModInt& operator += (const ModInt &_) { adj(x += _.x - mod); return *this; } ModInt& operator -= (const ModInt &_) { adj(x -= _.x); return *this; } ModInt& operator *= (const ModInt &_) { x = (LL)x * _.x % mod; return *this; } ModInt operator + (const ModInt &_) const { ModInt res = x; res += _; return res; } ModInt operator - (const ModInt &_) const { ModInt res = x; res -= _; return res; } ModInt operator * (const ModInt &_) const { ModInt res = x; res *= _; return res; } } f[N][N][6]; int main () { read(n, m); scanf("%s", s + 1); for (int i = 1; i <= n; ++i) f[i][i - 1][0] = 1; for (int k = 0; k < n; ++k) for (int i = 1, j = i + k; j <= n; ++i, ++j) { if (k + 1 <= m && (s[j] == '*' || s[j] == '?')) f[i][j][0] = f[i][j - 1][0]; if (k) { if ((s[i] == '(' || s[i] == '?') && (s[j] == ')' || s[j] == '?')) f[i][j][1] = f[i + 1][j - 1][0] + f[i + 1][j - 1][2] + f[i + 1][j - 1][3] + f[i + 1][j - 1][4]; for (int t = i; t < j; ++t) { f[i][j][2] += f[i][t][3] * f[t + 1][j][0]; f[i][j][3] += (f[i][t][2] + f[i][t][3]) * f[t + 1][j][1]; f[i][j][4] += (f[i][t][4] + f[i][t][5]) * f[t + 1][j][1]; f[i][j][5] += f[i][t][4] * f[t + 1][j][0]; } } f[i][j][5] += f[i][j][0]; f[i][j][3] += f[i][j][1]; } write(f[1][n][3]()); return 0; }
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