結果

問題 No.1269 I hate Fibonacci Number
ユーザー 沙耶花沙耶花
提出日時 2020-10-23 23:53:56
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 46 ms / 3,000 ms
コード長 18,761 bytes
コンパイル時間 3,297 ms
コンパイル使用メモリ 227,084 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-21 13:55:10
合計ジャッジ時間 4,561 ms
ジャッジサーバーID
(参考情報)
judge1 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 4 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 3 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 3 ms
5,376 KB
testcase_13 AC 3 ms
5,376 KB
testcase_14 AC 40 ms
5,376 KB
testcase_15 AC 6 ms
5,376 KB
testcase_16 AC 42 ms
5,376 KB
testcase_17 AC 3 ms
5,376 KB
testcase_18 AC 46 ms
5,376 KB
testcase_19 AC 28 ms
5,376 KB
testcase_20 AC 8 ms
5,376 KB
testcase_21 AC 26 ms
5,376 KB
testcase_22 AC 22 ms
5,376 KB
testcase_23 AC 25 ms
5,376 KB
testcase_24 AC 14 ms
5,376 KB
testcase_25 AC 15 ms
5,376 KB
testcase_26 AC 3 ms
5,376 KB
testcase_27 AC 2 ms
5,376 KB
testcase_28 AC 3 ms
5,376 KB
testcase_29 AC 13 ms
5,376 KB
testcase_30 AC 7 ms
5,376 KB
testcase_31 AC 17 ms
5,376 KB
testcase_32 AC 17 ms
5,376 KB
testcase_33 AC 4 ms
5,376 KB
testcase_34 AC 3 ms
5,376 KB
testcase_35 AC 5 ms
5,376 KB
testcase_36 AC 2 ms
5,376 KB
testcase_37 AC 3 ms
5,376 KB
testcase_38 AC 4 ms
5,376 KB
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 #

#include <stdio.h>
#include <bits/stdc++.h>


#include <utility>

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m`
    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (long long a : {2, 7, 61}) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace internal

}  // namespace atcoder


#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder

#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }
    static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

using namespace atcoder;
using mint = modint1000000007;
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf 1000000000000000000
long long L,R;
vector<string> get(vector<long long> F){
	vector<string> S;
	rep(i,F.size()){
		S.push_back(to_string(F[i]));
	}
	while(true){
		bool f = false;
		rep(i,S.size()){
			rep(j,S.size()){
				if(j<=i)continue;
				rep(k,S[j].size()){
					if(k+S[i].size()>S[j].size())break;
					if(S[j].substr(k,S[i].size())==S[i]){
						S.erase(S.begin()+j);
						f=true;
						break;
					}
				}
				if(f)break;
			}
			if(f)break;
		}
		if(!f)break;
	}
	return S;
}
vector<mint> dp,ndp;
template <typename T>
struct trie{
	T init_value;
	struct node{
		vector<int> next;
		T v;
		T sum;
		int depth;
		node(int wordSize,T iv,int d){
			next.resize(wordSize,-1);
			v = iv;
			sum = iv;
			depth = d;
		}
		
		int link=-1;
	};
	vector<node> nodes;

	int wordSize;
	trie(int sz,T iv){
		init_value = iv;
		wordSize = sz;
		nodes.push_back(node(wordSize,init_value,0));
	}
	
	void add(string &S,T x,int cPos=0,int cNode=0){
		if(cPos==S.size()){
			nodes[cNode].v = func(nodes[cNode].v,x);
			return;
		}
		int c = encode(S[cPos]);
		if(nodes[cNode].next[c]==-1){
			nodes[cNode].next[c] = nodes.size();
			nodes.push_back(node(wordSize,init_value,nodes[cNode].depth+1));
		}
		
		int nextNode = nodes[cNode].next[c];
		add(S,x,cPos+1,nextNode);
	}
	
	void set_link(){
		nodes[0].link = 0;
		queue<int> Q;
		Q.push(0);
		while(Q.size()!=0){
			int now = Q.front();
			Q.pop();
			nodes[now].v = func(nodes[now].v,nodes[nodes[now].link].v);
			nodes[now].sum = func(nodes[now].sum,nodes[now].v);
			for(int i=0;i<wordSize;i++){
				int to = nodes[now].next[i];
				if(to==-1)continue;
				int x = now;
				while(x!=0){
					x = nodes[x].link;
					if(nodes[x].next[i]!=-1){
						x = nodes[x].next[i];
						break;
					}
				}
				nodes[to].link = x;
				nodes[to].sum = func(nodes[to].sum,nodes[now].sum);
				Q.push(to);
			}
		}
	}
	
	T query(string &S,int cPos = 0,int cNode=0){
		T ret = init_value;
		if(cPos==S.size())return ret;
		int c = encode(S[cPos]);
		
		int nextNode = nodes[cNode].next[c];
		if(nextNode==-1){
			if(nodes[cNode].link!=-1){
				if(cNode!=0)ret = func(ret,query(S,cPos,nodes[cNode].link));
				else ret = func(ret,query(S,cPos+1,cNode));
			}
		}
		else{
			ret = func(ret,nodes[nextNode].v);
			ret = func(ret,query(S,cPos+1,nextNode));
		}
		
		return ret;
		
	}
	
	void go(){
		rep(i,nodes.size()){
			rep(j,10){
				int cNode = i;
				int nextNode = nodes[cNode].next[j];
				while(nextNode == -1){
					if(nodes[cNode].link==-1){
						nextNode = 0;
						break;
					}
					else{
						cNode = nodes[cNode].link;
						nextNode = nodes[cNode].next[j];
						if(nextNode==-1 && cNode==0){
							nextNode = 0;
							break;
						}
					}
				}
				ndp[nextNode] += dp[i];
			}
		}
		
		rep(i,nodes.size()){
			if(nodes[i].v<0){
				ndp[i] = 0;
			}
		}
	}
	
	int encode(char c){
		return c-'0';
	}
	
	T func(T a,T b){
		return a+b;
	}
	
};

int main(){	
	int N;
	cin>>N>>L>>R;
	vector<long long> F(2,1);
	
	while(true){
		if(F.back() > R){
			F.pop_back();
			break;
		}
		F.push_back(F.back() + F[F.size()-2]);
	}
	
	while(F.size()>0&&F[0] < L)F.erase(F.begin());
	
	vector<string> S = get(F);
	mint ans = 0;
	if(S.size()==0){
		ans = 1;
		rep(i,N)ans *= 10;
		ans--;
	}
	else{
		
	
		trie<int> T(10,0);
		
		rep(i,S.size()){
			T.add(S[i],-1);
		}
		T.set_link();
		dp.resize(T.nodes.size(),0);
		dp[0] = 1;

		rep(i,N){
			ndp.assign(T.nodes.size(),0);
			T.go();
			swap(dp,ndp);
		}
		
		
		rep(i,dp.size())ans += dp[i];
		
		ans --;
	}
	
	cout<<ans.val()<<endl;
	
    return 0;
}
0