import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.range, 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[0]; tokens.popFront; return token; } int readInt() { return readToken().to!int; } long readLong() { return readToken().to!long; } real readReal() { return readToken().to!real; } void chmin(T)(ref T t, in T f) { if (t > f) t = f; } void chmax(T)(ref T t, in T f) { if (t < f) t = f; } int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = cast(int)(as.length); for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a < val)); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a <= val)); } debug{ long counter; } // a^-1 (mod 2^64) long modInv(long a) in { assert(a & 1, "modInv: a must be odd"); } do { long b = ((a << 1) + a) ^ 2; b *= 2 - a * b; b *= 2 - a * b; b *= 2 - a * b; b *= 2 - a * b; return b; } // a^-1 (mod m) long modInv(long a, long m) in { assert(m > 0, "modInv: m > 0 must hold"); } do { long b = m, x = 1, y = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1"); if (b == -1) { y = -y; } return (y < 0) ? (y + m) : y; } x -= t * y; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1"); if (a == -1) { x = -x; } return (x < 0) ? (x + m) : x; } y -= t * x; } } // 2^-31 a (mod M) long montgomery(long M)(long a) if (1 <= M && M <= 0x7fffffff && (M & 1)) in { assert(0 <= a && a < (M << 31), "montgomery: 0 <= a < 2^31 M must hold"); } do { enum negInvM = -modInv(M) & 0x7fffffff; const b = (a + ((a * negInvM) & 0x7fffffff) * M) >> 31; return (b >= M) ? (b - M) : b; } // FFT on Z / M Z with Montgomery multiplication (x -> 2^31 x) // G: primitive 2^K-th root of unity class FFT(long M, int K, long G) if (is(typeof(montgomery!(M)(0))) && K >= 0 && 0 < G && G < M) { import std.algorithm : swap; import core.bitop : bsf; int n, invN; long[] g; this(int n) in { assert(!(n & (n - 1)), "FFT.this: n must be a power of 2"); assert(4 <= n && n <= 1 << K, "FFT.this: 4 <= n <= 2^K must hold"); } do { this.n = n; this.invN = ((1L << 31) / n) % M; g.length = n + 1; g[0] = (1L << 31) % M; g[1] = (G << 31) % M; foreach (_; 0 .. K - bsf(n)) { g[1] = montgomery!(M)(g[1] * g[1]); } foreach (i; 2 .. n + 1) { g[i] = montgomery!(M)(g[i - 1] * g[1]); } assert(g[0] != g[n >> 1] && g[0] == g[n], "FFT.this: G must be a primitive 2^K-th root of unity"); for (int i = 0, j = 0; i < n >> 1; ++i) { if (i < j) { swap(g[i], g[j]); swap(g[n - i], g[n - j]); } for (int m = n >> 1; (m >>= 1) && !((j ^= m) & m); ) {} } } void fftMontgomery(long[] x, bool inv) in { assert(x.length == n, "FFT.fftMontgomery: |x| = n must hold"); } do { foreach_reverse (h; 0 .. bsf(n)) { const l = 1 << h; foreach (i; 0 .. n >> 1 >> h) { const gI = g[inv ? (n - i) : i]; foreach (j; i << 1 << h .. ((i << 1) + 1) << h) { debug{ ++counter; } const t = montgomery!(M)(gI * x[j + l]); if ((x[j + l] = x[j] - t) < 0) { x[j + l] += M; } if ((x[j] += t) >= M) { x[j] -= M; } } } } for (int i = 0, j = 0; i < n; ++i) { if (i < j) { swap(x[i], x[j]); } for (int m = n; (m >>= 1) && !((j ^= m) & m); ) {} } if (inv) { foreach (i; 0 .. n) { x[i] = montgomery!(M)(invN * x[i]); } } } long[] convolution(long[] a, long[] b) in { assert(a.length <= n, "FFT.convolution: |a| <= n must hold"); assert(b.length <= n, "FFT.convolution: |b| <= n must hold"); } do { auto x = new long[n], y = new long[n]; foreach (i; 0 .. a.length) { const t = a[i] % M; x[i] = (((t < 0) ? (t + M) : t) << 31) % M; } foreach (i; 0 .. b.length) { const t = b[i] % M; y[i] = (((t < 0) ? (t + M) : t) << 31) % M; } fftMontgomery(x, false); fftMontgomery(y, false); foreach (i; 0 .. n) { x[i] = montgomery!(M)(x[i] * y[i]); } fftMontgomery(x, true); foreach (i; 0 .. n) { x[i] = montgomery!(M)(x[i]); } return x; } } // P0 P1 P2 > 2^90, P0 + P1 + P2 = 2^32 + 3 enum FFT_P0 = 2013265921L; // 2^27 15 + 1 enum FFT_P1 = 1811939329L; // 2^26 27 + 1 enum FFT_P2 = 469762049L; // 2^26 7 + 1 alias FFT0 = FFT!(FFT_P0, 27, 440564289L); // 31^15 alias FFT1 = FFT!(FFT_P1, 26, 72705542L); // 13^27 alias FFT2 = FFT!(FFT_P2, 26, 2187L); // 3^ 7 // Convolution of a and b (indices mod fft0.n) // modify a and b so that 0 <= a[i] < m, 0 <= b[i] < m long[] convolution(FFT0 fft0, FFT1 fft1, FFT2 fft2, long[] a, long[] b, long m) in { assert(fft0.n == fft1.n && fft0.n == fft2.n, "convolution: fft0.n = fft1.n = fft2.n must hold"); assert(1 <= m && m <= 0x7fffffff, "convolution: 1 <= m < 2^31 must hold"); } do { enum FFT_INV01 = modInv(FFT_P0, FFT_P1); enum FFT_INV012 = modInv(FFT_P0 * FFT_P1, FFT_P2); foreach (i; 0 .. a.length) { if ((a[i] %= m) < 0) { a[i] += m; } } foreach (i; 0 .. b.length) { if ((b[i] %= m) < 0) { b[i] += m; } } const x0 = fft0.convolution(a, b); const x1 = fft1.convolution(a, b); const x2 = fft2.convolution(a, b); auto x = new long[fft0.n]; foreach (i; 0 .. fft0.n) { auto y0 = x0[i] % FFT_P0; auto y1 = (FFT_INV01 * (x1[i] - y0 + FFT_P1)) % FFT_P1; auto y2 = (FFT_INV012 * ((x2[i] - y0 - FFT_P0 * y1) % FFT_P2 + FFT_P2)) % FFT_P2; x[i] = (y0 + FFT_P0 * y1 + ((FFT_P0 * FFT_P1) % m) * y2) % m; } return x; } // X^k mod f(X), coefficients in Z / m Z // f: monic (array length: deg f) long[] polyPower(long k, long[] f, long m) in { assert(k >= 0, "polyPower: k >= 0 must hold"); assert(f.length >= 1, "polyPower: deg f >= 1 must hold"); assert(1 <= m && m <= 0x7fffffff, "polyPower: 1 <= m < 2^31 must hold"); } do { import core.bitop : bsr; const n = cast(int)(f.length); auto fRev = new long[n + 1]; fRev[0] = 1; foreach (i; 1 .. n + 1) { fRev[i] = f[n - i]; } auto negInvFRev = [m - 1]; for (int l = 1; l < n; l <<= 1) { auto fft0 = new FFT0(l << 2), fft1 = new FFT1(l << 2), fft2 = new FFT2(l << 2); auto t = convolution(fft0, fft1, fft2, fRev[0 .. min(l << 1, n + 1)], negInvFRev, m)[0 .. l << 1]; t[0] += 2; negInvFRev = convolution(fft0, fft1, fft2, negInvFRev, t, m)[0 .. l << 1]; } auto a = new long[n]; if ((a[0] = 1) >= m) { a[0] -= m; } if (k > 0) { int nn; for (nn = 4; nn < 2 * n; nn <<= 1) {} auto fft0 = new FFT0(nn), fft1 = new FFT1(nn), fft2 = new FFT2(nn); foreach_reverse (h; 0 .. bsr(k) + 1) { a = convolution(fft0, fft1, fft2, a, a, m); auto aRev = new long[n]; foreach (i; 0 .. n) { aRev[i] = a[2 * n - 1 - i]; } auto negRevQ = convolution(fft0, fft1, fft2, aRev, negInvFRev, m); auto negQ = new long[n]; foreach (i; 0 .. n) { negQ[i] = negRevQ[n - 1 - i]; } auto t = convolution(fft0, fft1, fft2, f, negQ, m); foreach (i; 0 .. n) { if ((a[i] += t[i]) >= m) { a[i] -= m; } } a.length = n; if ((k >> h) & 1) { a = [0L] ~ a; foreach (i; 0 .. n) { if (((a[i] -= a[n] * f[i]) %= m) < 0) { a[i] += m; } } a.length = n; } } } return a; } immutable MO = 10L^^9 + 7; immutable A = [2,3,5,7,11,13]; immutable B = [4,6,8,9,10,12]; long[] getPatterns(int num, in int[] die) { const lim = num * die.maxElement; auto dp = new long[][](num + 1, lim + 1); dp[0][0] = 1; foreach (d; die) { foreach (i; 0 .. num) foreach (j; d .. lim + 1) { (dp[i + 1][j] += dp[i][j - d]) %= MO; } } return dp[num]; } long N; int P, Q; void main() { try { for (; ; ) { debug{ counter=0; } N = readLong(); P = readInt(); Q = readInt(); auto patA = getPatterns(P, A); auto patB = getPatterns(Q, B); const d = (cast(int)(patA.length) - 1) + (cast(int)(patB.length) - 1); int dd; for (dd = 4; dd < d; dd <<= 1) {} auto pat = convolution(new FFT0(dd), new FFT1(dd), new FFT2(dd), patA, patB, MO); auto f = new long[d]; foreach (i; 0 .. d) { f[i] = -pat[d - i]; } debug { writeln(patA[0 .. min($, 30)]); writeln(patB[0 .. min($, 30)]); writeln(pat[0 .. min($, 30)]); writeln("d = ", d); } const res = polyPower(N + d - 1, f, MO); long ans = res.sum % MO; writeln(ans); debug{ writeln("counter = ",counter); stdout.flush; } } } catch (EOFException e) { } }