結果

問題 No.1085 桁和の桁和
コンテスト
ユーザー heno239
提出日時 2020-06-19 21:41:35
言語 C++14
(gcc 15.2.0 + boost 1.89.0)
結果
TLE  
実行時間 -
コード長 5,674 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 1,453 ms
コンパイル使用メモリ 121,924 KB
実行使用メモリ 59,284 KB
最終ジャッジ日時 2024-07-23 00:01:04
合計ジャッジ時間 5,077 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other TLE * 1 -- * 34
権限があれば一括ダウンロードができます

ソースコード

diff #
raw source code 

#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
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 pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> 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<ll> 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<poly> 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;
}
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