#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define reE(i,a,b) for(auto (i)=(a);(i)<=(b);(i)++) #define rE(i,b) reE(i,0,b) #define reT(i,a,b) for(auto (i)=(a);(i)<(b);(i)++) #define rT(i,b) reT(i,0,b) #define rep(i,a,b) reE(i,a,b); #define rev(i,a,b) for(auto (i)=(b)-1;(i)>=(a);(i)--) #define itr(i,b) for(auto (i)=(b).begin();(i)!=(b).end();++(i)) #define LL long long #define all(b) (b).begin(),(b).end() #define input_init stringstream ss; string strtoken, token; istringstream is #define input_line getline(cin, strtoken);is.str(strtoken);is.clear(istringstream::goodbit) #define input_token(num) ss.str(""); ss.clear(stringstream::goodbit); getline(is, token, ','); ss << token; ss >> num #define LL long long const LL mod = (LL) 1e9 + 7; #define MAX_LOGN 60 template struct Mr{ vector first; vector C; vector> bin; T zero, one; int M; //n(1,,,2M)をn(1,,,M)に修正、O(M^2) void form(vector &n){ rev(i, M + 1, 2 * M + 1){ reE(j, 1, M)n[i - j] = (n[i - j] + (C[M - j] * n[i])); n[i] = zero; } } //lとrを足し合わせる、O(M^2) void add(vector &l, vector &r, vector &ans){ reE(i, 1, 2 * M)ans[i] = zero; reE(i, 1, M)reE(j, 1, M)ans[i + j] = (ans[i + j] + (l[i] * r[j])); form(ans); } //初期化、O(M*MAX_LOGN) Mr(const vector& f, const vector& c, int m, T e1, T e0){ M = m; first.reserve(M + 1); C.reserve(M); zero = e0, one = e1; first.push_back(zero); rT(i, M){ first.push_back(f[i]); C.push_back(c[i]); } bin.resize(MAX_LOGN); rT(i, MAX_LOGN)bin[i].resize(2 * M + 1); rE(i, 2 * M)bin[0][i] = zero; bin[0][1] = one; reT(i, 1, MAX_LOGN){ add(bin[i - 1], bin[i - 1], bin[i]); } } //N項目の計算、戻り値がTの形であることに注意、O(M^2*logN) vector calc(LL n){ n--; vector tmp, result = bin[0]; for (int b = 0; n; b++, n >>= 1) if (1 & n){ tmp = result; add(tmp, bin[b], result); } T ans = zero; //reE(i, 1, M)ans = ans + (result[i] * first[i]); return result; } }; //テンプレート、デフォルトコンストラクタのオーバーロードを忘れない #define MOD 1000000007 struct X{ LL val; X(LL v){ val = v; } X(){ val = 0; } LL operator=(const X &another){ return val = another.val; } LL operator*(const X &another)const{ return (val*another.val) % MOD; } LL operator+(const X &another)const{ return (val + another.val) % MOD; } }; LL comb[1301]; LL temp2[100][1301][6] = { { {1} } }; LL temp1[100][1301][6]; LL dp[2601] = { 1 }; LL sumc[1301] = { 0 }; int sosuu[] = { 2, 3, 5, 7, 11, 13 }, gousei[] = { 4, 6, 8, 9, 10, 12 }; int p, c; void func1(int n){ if (n == c){ for (int i = 0; i < 1300; i++){ for (int j = 0; j < 6; j++) comb[i] = (comb[i] + temp1[n][i][j]) % MOD; } return; } for (int j = 0; j < 6; j++) for (int i = gousei[j]; i < 1300; i++){ for (int k = 0; k <= j; k++) temp1[n + 1][i][j] = (temp1[n + 1][i][j] + temp1[n][i - gousei[j]][k]) % MOD; } func1(n + 1); } void func2(int n){ if (n == p){ for (int i = 0; i < 1300; i++){ for (int j = 0; j < 6; j++) temp1[0][i][0] = (temp1[0][i][0] + temp2[n][i][j]) % MOD; } func1(0); return; } for (int j = 0; j < 6; j++) for (int i = sosuu[j]; i < 1300; i++){ for (int k = 0; k <= j; k++) temp2[n + 1][i][j] = (temp2[n + 1][i][j] + temp2[n][i - sosuu[j]][k]) % MOD; } func2(n + 1); } vector A(1300), C(1300); int main(void){ LL N; cin >> N >> p >> c; func2(0); for (int i = 0; i <= 2600; i++){ for (LL j = 1; j <= min(i,1300); j++){ dp[i] = (dp[i] + comb[j] * dp[i - j]) % MOD; } } for (int i = 0; i < 1300; i++){ A[i] = X(dp[i]); } for (int i = 1; i <= 1300; i++){ C[1300 - i] = X(comb[i]); } sumc[1300] = 0; for (int i = 1299; i >= 0; i--){ sumc[i] = (sumc[i + 1] + comb[i]) % MOD; } LL res = 0; if (N < 1400){ for (LL i = 0; i < min(N,1300ll); i++) { res = (res + dp[i] * sumc[min(N,1300ll) - i])%MOD; } } else{ Mr mr(A, C, 1300, X(1), X(0)); auto cc = mr.calc(N + 1 - 1300); for (LL i = 0; i < 1300; i++) if(sumc[1300-i]){ LL x = 0; for (int j = 0; j < 1300; j++){ x = (x + dp[i + j] * cc[j + 1].val) % MOD; } res = (res + x*sumc[1300 - i])%MOD; //cout << x <<" "<