int dfs(int position, int condition, bool boundary) {

     if (position < ) return (condition ?);

     if (condition < ) return ;

     if (!boundary && ~f[position][condition]) return f[position][condition];

     int respond = ;

     int top = boundary ? num[position] : ;

     for (int i = ; i <= top; ++i)

         respond += dfs(position - , new_s(condition, i), boundary && i == top);

     return boundary ? respond : f[position][condition] = respond;

 }

int dfs(int pos, int con, bool e) {

    if (pos < ) return (con ?);

    if (con < ) return ;

    if (!e && ~f[pos][con]) return f[pos][con];

    int res = ;

    int top = e ? num[pos] : ;

    for (int i = ; i <= top; ++i)

        res += dfs(pos - , new_s(con, i), e && i == top);

    return e ? res : f[pos][con] = res;

}