// #pragma GCC target ("avx") // #pragma GCC optimize("Ofast") // #pragma GCC optimize("unroll-loops") // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #include using namespace std; // #define int long long // #define endl '\n' #pragma region TEMPLATE /* TYPE */ typedef long long ll; typedef long double ld; typedef pair pii; typedef pair pll; typedef vector vpii; typedef vector vpll; typedef vector vi; typedef vector vl; typedef vector vst; typedef vector vb; typedef vector vld; typedef vector> vvi; template> using prique = priority_queue, Cmp>; template using prique_r = prique>; /* CONSTANT */ #define ln '\n' const int INF = 1 << 30; const ll INFF = 1LL << 60; const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const int MOD = 1e9 + 7; const int MODD = 998244353; const string alphabet = "abcdefghijklmnopqrstuvwxyz"; const double EPS = 1e-9; const ld PI = 3.14159265358979323846264338327950288; const int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1, 0 }; const int dy[] = { 0, 1, 0, -1, -1, -1, 1, 1, 0 }; /* CONTAINER */ #define PB emplace_back #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() #define SORT(v) sort(ALL(v)) #define RSORT(v) sort(RALL(v)) #define LESS(x, val) (lower_bound(x.begin(), x.end(), val) - x.begin()) #define LEQ(x, val) (upper_bound(x.begin(), x.end(), val) - x.begin()) #define GREATER(x, val) (int)(x).size() - LEQ((x), (val)) #define GEQ(x, val) (int)(x).size() - LESS((x), (val)) #define UNIQUE(v) sort(ALL(v)); (v).erase(unique(ALL(v)), (v).end()) template vector make_v(size_t a) { return vector(a); } template auto make_v(size_t a, Ts... ts) { return vector(ts...))>(a, make_v(ts...)); } template enable_if_t::value != 0> fill_v(U &u, const V... v) { u = U(v...); } template enable_if_t::value == 0> fill_v(U &u, const V... v) { for (auto &e : u) fill_v(e, v...); } /* LOOP */ #define _overload3(_1, _2, _3, name, ...) name #define _REP(i, n) REPI(i, 0, n) #define REPI(i, a, b) for (ll i = (ll)a; i < (ll)b; ++i) #define REP(...) _overload3(__VA_ARGS__, REPI, _REP,)(__VA_ARGS__) #define _RREP(i, n) RREPI(i, n, 0) #define RREPI(i, a, b) for (ll i = (ll)a; i >= (ll)b; --i) #define RREP(...) _overload3(__VA_ARGS__, RREPI, _RREP,)(__VA_ARGS__) #define EACH(e, v) for (auto& e : v) #define PERM(v) sort(ALL(v)); for (bool c##p = true; c##p; c##p = next_permutation(ALL(v))) /* INPUT */ template void SSS(T& t) { cin >> t; } template void SSS(Head&& head, Tail&&... tail) { cin >> head; SSS(tail...); } #define SS(T, ...) T __VA_ARGS__; SSS(__VA_ARGS__); #define SV(T, v, n) vector v(n); for (auto& i : v) cin >> i; #define SVV(T, v, n, m) vector> v(n, vector(m)); for (auto& r : v) for (auto& i : r) cin >> i; /* OUTPUT */ // Yes / No inline int YES(bool x) { cout << (x ? "YES" : "NO") << endl; return 0; } inline int Yes(bool x) { cout << (x ? "Yes" : "No") << endl; return 0; } inline int yes(bool x) { cout << (x ? "yes" : "no") << endl; return 0; } inline int yES(bool x) { cout << (x ? "yES" : "nO") << endl; return 0; } inline int Yay(bool x) { cout << (x ? "Yay!" : ":(") << endl; return 0; } // PROTOTYPE DECLARATION template ostream &operator<<(ostream &os, const pair &j); template ostream &operator<<(ostream &os, const tuple &t); template::value, decltype(declval().begin(), nullptr)> = nullptr> ostream& operator<<(ostream &os, const C &c); template ostream &operator<<(ostream &os, const stack &j); template ostream &operator<<(ostream &os, const queue &j); template ostream &operator<<(ostream &os, const priority_queue &j); // IMPLEMENTATION template ostream &operator<<(ostream &os, const pair &j) { return os << '{' << j.first << ", " << j.second << '}'; } template enable_if_t PRINT_TUPLE(ostream &os, const tuple &t) {} template enable_if_t PRINT_TUPLE(ostream &os, const tuple &t) { os << get(t); if (num + 1 < sizeof...(T)) os << ", "; PRINT_TUPLE(os, t); } template ostream &operator<<(ostream &os, const tuple &t) { PRINT_TUPLE(os << '{', t); return os << '}'; } template::value, decltype(declval().begin(), nullptr)>> ostream& operator<<(ostream &os, const C &c) { os << '{'; for (auto it = begin(c); it != end(c); it++) { if (begin(c) != it) os << ", "; os << *it; } return os << '}'; } template ostream &operator<<(ostream &os, const stack &j) { deque d; for (auto c = j; !c.empty(); c.pop()) d.push_front(c.top()); return os << d; } template ostream &operator<<(ostream &os, const queue &j) { deque d; for (auto c = j; !c.empty(); c.pop()) d.push_back(c.front()); return os << d; } template ostream &operator<<(ostream &os, const priority_queue &j) { deque d; for (auto c = j; !c.empty(); c.pop()) d.push_front(c.top()); return os << d; } // OUTPUT FUNCTION template int PV(T &v) { int sz = v.size(); for (int i = 0; i < sz; ++i) cout << v[i] << " \n"[i == sz - 1]; return 0; } inline int print() { cout << endl; return 0; } template int print(Head&& head){ cout << head; return print(); } template int print(Head&& head, Tail&&... tail) { cout << head << " "; return print(forward(tail)...); } #ifdef LOCAL inline void dump() { cerr << endl; } template void dump(Head&& head) { cerr << head; dump(); } template void dump(Head&& head, Tail&&... tail) { cerr << head << ", "; dump(forward(tail)...); } #define debug(...) do {cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; dump(__VA_ARGS__); } while (false) #else #define dump(...) #define debug(...) #endif /* OTHER */ #define fi first #define se second #define MP make_pair #define MT make_tuple #define tmax(x, y, z) max((x), max((y), (z))) #define tmin(x, y, z) min((x), min((y), (z))) template inline bool between(T x, A a, B b) { return ((a <= x) && (x < b)); } template inline bool chmax(A &a, const B &b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A &a, const B &b) { if (a > b) { a = b; return true; } return false; } inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; } inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; } inline ll POW(ll a, ll b) { ll r = 1; do { if (b & 1) r *= a; a *= a; } while (b >>= 1); return r; } struct abracadabra { abracadabra() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); cerr << fixed << setprecision(5); }; } ABRACADABRA; #pragma endregion #pragma region math modint /** * @brief ModInt * @docs docs/math/modint.md */ template< int MODULO > struct ModInt { using i32 = int; using i64 = long long; using u32 = unsigned int; using u64 = unsigned long long; u64 x; ModInt() : x(0) {} ModInt(i64 y) : x(set(y % MODULO + MODULO)) {} static u64 set(const i64 &y) { return (y < MODULO) ? y : y - MODULO; } ModInt operator+(const ModInt &m) const { return ModInt(set(x + m.x)); } ModInt operator-(const ModInt &m) const { return ModInt(set(x + MODULO - m.x)); } ModInt operator*(const ModInt &m) const { return ModInt(x * m.x % MODULO); } ModInt operator/(const ModInt &m) const { return ModInt(x) * ~ModInt(m.x); } ModInt &operator+=(const ModInt &m) { return *this = *this + m; } ModInt &operator-=(const ModInt &m) { return *this = *this - m; } ModInt &operator*=(const ModInt &m) { return *this = *this * m; } ModInt &operator/=(const ModInt &m) { return *this = *this / m; } ModInt &operator^=(const u64 &y) { return *this = *this ^ y; } ModInt operator~ () const { return *this ^ (MODULO - 2); } ModInt operator- () const { return ModInt(set(MODULO - x)); } ModInt operator! () const { return getFact(u32(*this)); } ModInt operator& () const { return getFinv(u32(*this)); } ModInt operator++() { return *this = ModInt(set(x + 1)); } ModInt operator--() { return *this = ModInt(set(x + MODULO - 1)); } bool operator==(const ModInt &m) const { return x == m.x; } bool operator!=(const ModInt &m) const { return x != m.x; } bool operator< (const ModInt &m) const { return x < m.x; } bool operator<=(const ModInt &m) const { return x <= m.x; } bool operator> (const ModInt &m) const { return x > m.x; } bool operator>=(const ModInt &m) const { return x >= m.x; } explicit operator u64() const { return x; } ModInt operator^(i64 y) const { return pow(x, y); } static ModInt pow(i64 x, i64 y) { bool neg = false; if (y < 0) y = -y, neg = true; ModInt u(1), t(x); while (y) { if (y & 1) u *= t; t *= t; y >>= 1; } return neg ? ModInt(1) / u : u; } friend ostream &operator<<(ostream &os, const ModInt< MODULO > &m) { return os << m.x; } friend istream &operator>>(istream &is, ModInt< MODULO > &m) { u64 y; is >> y; m = ModInt(y); return is; } static vector< ModInt > fact, finv, invs; static void init(u32 n) { u32 m = fact.size(); if (n < m) return; fact.resize(n + 1, 1); finv.resize(n + 1, 1); invs.resize(n + 1, 1); if (m == 0) m = 1; for (u32 i = m; i <= n; ++i) fact[i] = fact[i - 1] * ModInt(i); finv[n] = ModInt(1) / fact[n]; for (u32 i = n; i >= m; --i) finv[i - 1] = finv[i] * ModInt(i); for (u32 i = m; i <= n; ++i) invs[i] = finv[i] * fact[i - 1]; } static ModInt getFact(u32 n) { init(n); return fact[n]; } static ModInt getFinv(u32 n) { init(n); return finv[n]; } static ModInt getInvs(u32 n) { init(n); return invs[n]; } static ModInt C(i64 n, i64 r) { if (r == 0) return ModInt(1); if (r < 0) return ModInt(0); if (n < 0) return ModInt(r & 1 ? MODULO - 1 : 1) * C(-n + r - 1, r); if (n == 0 || n < r) return ModInt(0); init(n); return fact[n] * finv[n - r] * finv[r]; } static ModInt P(i64 n, i64 r) { if (n < r || r < 0) return ModInt(0); init(n); return fact[n] * finv[n - r]; } static ModInt H(i64 n, i64 r) { if (n < 0 || r < 0) return ModInt(0); if (!n && !r) return ModInt(1); init(n + r - 1); return C(n + r - 1, r); } static ModInt montmort(u32 n) { ModInt res; init(n); for (u32 k = 2; k <= n; ++k) { if (k & 1) res -= finv[k]; else res += finv[k]; } return res *= fact[n]; } static ModInt LagrangePolynomial(vector &y, i64 t) { u32 n = y.size() - 1; if (t <= n) return y[t]; init(n + 1); ModInt res, num(1); for (int i = 0; i <= n; ++i) num *= ModInt(t - i); for (int i = 0; i <= n; ++i) { ModInt tmp = y[i] * num / (ModInt(t - i)) * finv[i] * finv[n - i]; if ((n - i) & 1) res -= tmp; else res += tmp; } return res; } }; template< int MODULO > vector> ModInt< MODULO >::fact = vector>(); template< int MODULO > vector> ModInt< MODULO >::finv = vector>(); template< int MODULO > vector> ModInt< MODULO >::invs = vector>(); constexpr int MODULO = (int)1e9 + 7; using modint = ModInt< MODULO >; #pragma endregion // mod 9 modint dp[100100][10]; signed main() { SS(string, S); SS(int, D); int N = S.size(); if (D == 0) { int _0 = 0, _1 = 0; REP(i, N) { if (S[i] == '0') ++_0; if (S[i] == '?') ++_1; if (_0 + _1 != N) return print(0); return print(modint::pow(2, _1)); } } dp[0][0] = 1; REP(i, N) { REP(j, 9) { if (S[i] == '?') { REP(k, 10) { dp[i + 1][(j + k) % 9] += dp[i][j]; } } else { int dig = S[i] - '0'; dp[i + 1][(j + dig) % 9] += dp[i][j]; } } } if (D != 9) print(dp[N][D % 9]); else { modint res = dp[N][0]; int _0 = 0, _1 = 0; REP(i, N) { if (S[i] == '0') ++_0; if (S[i] == '?') ++_1; } if (_0 + _1 == N) { res -= 1; } print(res); } }