#define _USE_MATH_DEFINES #include "bits/stdc++.h" using namespace std; #define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i)) #define rep(i,j) FOR(i,0,j) #define each(x,y) for(auto &(x):(y)) #define mp make_pair #define MT make_tuple #define all(x) (x).begin(),(x).end() #define debug(x) cout<<#x<<": "<<(x)< >(b,vector(c,d)) #define vvv(a,b,c,d,e) vector > >(b,vv(a,c,d,e)) using ll = long long; using pii = pair; using vi = vector; using vll = vector; const int MOD = (int)1e9 + 7; vector > mulMatMod(const vector > &A, const vector > &B) { auto n = A.size(), m = A[0].size(), p = B[0].size(); vector > res(n, vector(p)); for (int i = 0; i < n; ++i)for (int j = 0; j < p; ++j) for (int k = 0; k < m; ++k) res[i][j] = (int)((res[i][j] + (long long)A[i][k] * B[k][j]) % MOD); return res; } vector > powMatMod(vector > A, long long k) { auto n = A.size(); vector > res(n, vector(n)); for (int i = 0; i < n; ++i)res[i][i] = 1; while (k) { if (k % 2)res = mulMatMod(res, A); k /= 2; A = mulMatMod(A, A); } return res; } template class ModInt { public: ModInt() :value(0) {} ModInt(long long val) :value((int)(val<0 ? MOD + val%MOD : val%MOD)) { } ModInt& operator+=(ModInt that) { value = value + that.value; if (value >= MOD)value -= MOD; return *this; } ModInt& operator-=(ModInt that) { value -= that.value; if (value<0)value += MOD; return *this; } ModInt& operator*=(ModInt that) { value = (int)((long long)value * that.value % MOD); return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt pow(long long k) const { if (value == 0)return 0; ModInt n = *this, res = 1; while (k) { if (k & 1)res *= n; n *= n; k >>= 1; } return res; } ModInt inverse() const { long long a = value, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } return ModInt(u); } int toi() const { return value; } private: int value; }; typedef ModInt<1000000007> mint; ostream& operator<<(ostream& os, const mint& x) { os << x.toi(); return os; } mint g(int b, int d) { vector A(3, vi(3)); A[0][0] = d + 1; A[0][1] = d; A[1][1] = A[1][2] = A[2][2] = 1; A = powMatMod(A, b); RT mint(A[0][1]) + mint(A[0][2]); } ll powll(ll x, ll k) { ll re = 1; while (k > 0) { if (k & 1)re *= x; k >>= 1; x *= x; } RT re; } ll num(int b, int d) { if (pow(d + 1.0, b) - 1 > (int)2e9)RT(int)1e9 + 1; RT powll(d+1ll, b) - 1; } mint f(int b, int d, int n) { if (n <= 0)RT 0; int lb = 1, ub = b + 1; while (ub - lb > 1) { int mid = (lb + ub) / 2; if (n <= num(mid - 1, d))ub = mid; else lb = mid; } b = lb; ll m = num(b - 1, d); mint gg = g(b - 1, d); n -= (int)m; mint re = (gg + b)*(n / (m + 1)) + gg; n %= (m + 1); if (n > 0) { re += b; n--; } if (n > 0)re += f(b - 1, d, n); RT re; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20); int N, B, D; while (cin >> N >> B >> D) { mint re = g(B, D); re -= f(B, D, N); cout << re << endl; } }