import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } /* a[0] = 0 a[i] = (D + 1) a[i - 1] + D i a[i] - 2 a[i - 1] + a[i - 2] = (D + 1) a[i - 1] - 2 (D + 1) a[i - 2] + (D + 1) a[i - 3] T^3 - (D + 3) T^2 + (2 D + 3) T - (D + 1) */ enum MO = 10L^^9 + 7; enum INF = 3 * 10L^^18; enum LIM = 100; long[] mul(long[] a, long[] b, long D) { auto c = new long[5]; foreach (i; 0 .. 3) foreach (j; 0 .. 3) { c[i + j] += a[i] * b[j]; } c[] %= MO; foreach_reverse (i; 3 .. 5) { c[i - 1] = (c[i - 1] + ( D + 3) * c[i]) % MO; c[i - 2] = (c[i - 2] - (2 * D + 3) * c[i]) % MO; c[i - 3] = (c[i - 3] + ( D + 1) * c[i]) % MO; } return c[0 .. 3]; } long getFull(long k, long D) { debug { enum lim = 10; auto a = new long[lim]; a[0] = 0; foreach (i; 1 .. lim) { a[i] = ((D + 1) * a[i - 1] + D * i) % MO; } writeln(a); foreach (i; 3 .. lim) { assert((a[i] - (D + 3) * a[i - 1] + (2 * D + 3) * a[i - 2] - (D + 1) * a[i - 3]) % MO == 0); } } long[] x = [0, 1, 0], y = [1, 0, 0]; for (long e = k; e; e >>= 1) { if (e & 1) { y = mul(y, x, D); } x = mul(x, x, D); } const a2 = ((D + 1) * D + D * 2) % MO; const ret = (y[1] * D + y[2] * a2) % MO; debug { writeln("getFull ", k, " ", D, " = ", ret); } return ret; } long[] len; long calc(int k, long D, long a, long b) { chmax(a, 0); chmin(b, len[k]); if (a >= b) { return 0; } long ret; if (a == 0 && b == len[k]) { ret = getFull(k, D); } else { const m = len[k - 1] + 1; if (a / m == b / m) { ret = calc(k - 1, D, a % m, b % m); } else { ret += calc(k - 1, D, a % m, m - 1); ret += (b / m - a / m - 1) * getFull(k - 1, D); ret += (b / m - a / m) * k; ret += calc(k - 1, D, 0, b % m); ret %= MO; } } debug { writeln("calc ", k, " ", D, " ", a, " ", b, " = ", ret); } return ret; } void main() { try { for (; ; ) { const N = readLong(); const B = readLong(); const D = readLong(); len = new long[LIM]; len[0] = 0; foreach (i; 1 .. LIM) { len[i] = cast(long)(min((D + 1) * BigInt(len[i - 1]) + D, BigInt(INF))); } debug { writeln("len = ", len); } long ans = getFull(B, D); foreach (i; 0 .. LIM) { if (N <= len[i]) { ans -= calc(i, D, 0, N); break; } } ans = (ans % MO + MO) % MO; writeln(ans); } } catch (EOFException e) { } }