#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef long double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acos(-1.0); ll mod_pow(ll x, ll n) { ll res = 1; while (n) { if (n & 1)res = res * x%mod; x = x * x%mod; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n%mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint &a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint &a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint &a, modint b) { a.n = ((ll)a.n*b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, int n) { if (n == 0)return modint(1); modint res = (a*a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p%a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } ll mod_pow(ll a, ll n, ll m) { if (a >= m)a %= m; ll res = 1; while (n) { if (n & 1)res = res * a%m; a = a * a%m; n >>= 1; } return res; } ll root[24], invroot[24]; void init(const ll &p) { rep(i, 24) { int n = (1 << i); root[i] = mod_pow(3, (p - 1) / n, p); invroot[i] = mod_pow(root[i], p - 2, p); } } typedef vector poly; poly dft(poly f, bool inverse, const ll &p) { int n = f.size(); int i, j, k; //bit左右反転 for (i = 0, j = 1; j < n - 1; j++) { for (k = n >> 1; k >(i ^= k); k >>= 1); if (i > j)swap(f[i], f[j]); } for (int j = 1; (1 << j) <= n; j++) { int m = 1 << j; ll zeta = root[j]; if (inverse)zeta = invroot[j]; for (i = 0; i < n; i += m) { ll powzeta = 1; for (k = i; k < i + m / 2; k++) { ll t1 = f[k], t2 = powzeta * f[k + m / 2] % p; f[k] = t1 + t2; while (f[k] >= p)f[k] -= p; f[k + m / 2] = t1 - t2 + p; while (f[k + m / 2] >= p)f[k + m / 2] -= p; (powzeta *= zeta) %= p; } } } if (inverse) { ll rv = mod_pow(n, p - 2, p); for (i = 0; i < n; i++) { (f[i] *= rv) %= p; } } return f; } poly multi(poly &g, poly &h, const ll &p, int n) { init(p); poly gg = dft(g, false, p); poly hh = dft(h, false, p); poly ff; ff.resize(n); rep(i, n) { ff[i] = gg[i] * hh[i] % p; } return dft(ff, true, p); } constexpr ll m0 = 469762049; constexpr ll m1 = 167772161; constexpr ll m2 = 595591169; ll inv01 = mod_pow(m0, m1 - 2, m1); ll inv012 = mod_pow(m0 * m1, m2 - 2, m2); ll calc(ll &a, ll &b, ll &c, const ll &p) { ll res = 0; ll x1 = a; ll x2 = (b - x1)*inv01; x2 %= m1; if (x2 < 0)x2 += m1; ll x3 = (c - x1 - x2 * m0) % m2 * inv012; x3 %= m2; if (x3 < 0)x3 += m2; res = x1 + x2 * m0 % p + x3 * m0 % p*m1; return res % p; } poly multiply(poly g, poly h, const ll &p) { int resz = g.size() + h.size() - 1; int n = 1; int pi = 0, qi = 0; rep(i, g.size())if (g[i])pi = i; rep(i, h.size())if (h[i])qi = i; int sz = pi + qi + 2; while (n < sz)n *= 2; g.resize(n); h.resize(n); vector vp(3); vp[0] = multi(g, h, m0, n); vp[1] = multi(g, h, m1, n); vp[2] = multi(g, h, m2, n); poly res(resz); rep(i, res.size()) { ll a, b, c; if (i < vp[0].size())a = vp[0][i]; else a = 0; if (i < vp[1].size())b = vp[1][i]; else b = 0; if (i < vp[2].size())c = vp[2][i]; else c = 0; res[i] = calc(a, b, c, p); } return res; } int f[1000000]; void init_k() { rep(i, 1000000) { if (i < 10)f[i] = i; else { int s = 0; int cop = i; while (cop > 0) { s += cop % 10; cop /= 10; } f[i] = f[s]; } } } void solve() { string s; int d; cin >> s >> d; int le = 0; int cnt = 0; for (char c : s) { if (c == '?')cnt++; else le += c - '0'; } poly b(10, 1); poly x = { 1 }; while (cnt > 0) { if (cnt & 1) { x = multiply(x, b, mod); } cnt >>= 1; if (cnt == 0)break; b = multiply(b, b, mod); } modint ans = 0; rep(i, x.size()) { if (f[i + le]==d) { ans += x[i]; } } cout << ans << "\n"; } signed main() { //ios::sync_with_stdio(false); //cin.tie(0); //cout << fixed << setprecision(10); //init_f(); init_k(); //int t; cin >> t; rep(i, t) solve(); stop return 0; }