package q4xx; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class Q444_5 { InputStream is; PrintWriter out; String INPUT = ""; // String INPUT = "100000 8 12"; // String INPUT = "6 2 0"; static final int mod = 1000000007; void solve() { superPrepare(); long n = nl(); int P = ni(), C = ni(); long[] pp = make(new int[]{2, 3, 5, 7, 11, 13}, P); long[] cc = make(new int[]{4, 6, 8, 9, 10, 12}, C); long[] co = rstrip(convolute(pp, cc, 3, mod)); for(int i = 0, j = co.length-1;i < j;i++,j--){ long d = co[i]; co[i] = co[j]; co[j] = d; } co = Arrays.copyOf(co, co.length-1); long[] xco = lr(co, co.length-1+n); long ret = 0; for(long v : xco)ret += v; out.println(ret%mod); } static long[] rstrip(long[] a) { for(int i = a.length-1;i >= 0;i--){ if(a[i] != 0)return Arrays.copyOf(a, i+1); } return new long[0]; } long[] make(int[] ps, int P) { int max = P*ps[ps.length-1]; int[][] dp = new int[max+1][6]; dp[0][0] = 1; for(int k = 0;k < P;k++){ for(int i = max;i >= 0;i--){ long s = 0; for(int j = 0;j < 6;j++){ s += dp[i][j]; if(s >= mod)s -= mod; dp[i][j] = 0; if(i+ps[j] <= max){ dp[i+ps[j]][j] += s; if(dp[i+ps[j]][j] >= mod)dp[i+ps[j]][j] -= mod; } } } } long[] ret = new long[max+1]; for(int i = 0;i <= max;i++){ for(int j = 0;j < 6;j++){ ret[i] += dp[i][j]; } ret[i] %= mod; } return ret; } public static long f(long[] a, long[] co) { long big = 8L*mod*mod; long s = 0; for(int i = 0;i < co.length;i++){ s += co[i] * a[i]; if(s >= big)s -= big; } return s % mod; } static long[] rev(long[] a) { for(int i = 0, j = a.length-1;i < j;i++,j--){ long d = a[i]; a[i] = a[j]; a[j] = d; } return a; } public static long[] lr(long[] co, long n) { int m = co.length; if(m == 0)return new long[0]; if(m == 1){ long ret = 1; long mul = co[0]; for(;n > 0;n >>>= 1){ if((n&1)==1)ret = ret * mul % mod; mul = mul * mul % mod; } return new long[]{ret}; } long[] gf = new long[m+1]; // Generating Function of co for(int i = 0;i < m;i++){ gf[i+1] = (mod-co[m-1-i]) % mod; } gf[0] = 1; long[] rigf = rev(inv(gf)); int mm = Math.max(2, Integer.highestOneBit(m-1)<<2); long[][] frigf = new long[3][]; for(int k = 0;k < 3;k++){ int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; frigf[k] = nttmb(rigf, mm, false, P, g, k); } long[][] fco = new long[3][]; for(int k = 0;k < 3;k++){ int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; fco[k] = nttmb(co, mm, false, P, g, k); } long K = Integer.highestOneBit(mod)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/mod; long[] ret = new long[m]; ret[0] = 1; int h = 63-Long.numberOfLeadingZeros(n); int hh = h*6/7; int las = m-1; while(co[las] == 0)las--; for(int u = 0;u < n>>>hh;u++){ long r = ret[m-1]; for(int i = m-1;i > las;i--){ ret[i] = ret[i-1]; } for(int i = las;i >= 1;i--){ ret[i] = modh(r * co[i] + ret[i-1], M, H, mod); } ret[0] = modh(r * co[0], M, H, mod); } for(int l = hh-1;l >= 0;l--){ long[] ltemp = convolute(ret, ret, 3, mod, null); long[] fu = convolute(Arrays.copyOfRange(ltemp, m, 2*m), rigf, 3, mod, frigf); long[] last = convolute(Arrays.copyOfRange(fu, m, 2*m), co, 3, mod, fco); for(int i = 0;i < m;i++){ ret[i] = last[i] + ltemp[i]; if(ret[i] >= mod)ret[i] -= mod; } if(n<<~l<0){ // +1 long r = ret[m-1]; for(int i = m-1;i > las;i--){ ret[i] = ret[i-1]; } for(int i = las;i >= 1;i--){ ret[i] = modh(r * co[i] + ret[i-1], M, H, mod); } ret[0] = modh(r * co[0], M, H, mod); } } return ret; } // public static long[] mul(long[] a, long[] b, int lim) // { // return Arrays.copyOf(NTTCRT.convoluteSimply(a, b, mod, G), lim); // } public static long[] mul(long[] a, long[] b, int lim) { return Arrays.copyOf(convolute(a, b, 3, mod), lim); } // F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x) public static long[] inv(long[] p) { int n = p.length; long[] f = {invl(p[0], mod)}; for(int i = 0;i < p.length;i++){ if(p[i] == 0)continue; p[i] = mod-p[i]; } for(int i = 1;i < 2*n;i*=2){ long[] f2 = mul(f, f, Math.min(n, 2*i)); long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2*i)); for(int j = 0;j < f.length;j++){ f2p[j] += 2L*f[j]; if(f2p[j] >= mod)f2p[j] -= mod; if(f2p[j] >= mod)f2p[j] -= mod; } f = f2p; } return f; } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681}; public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17}; // public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033}; // public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5}; static long F = 1051721729L * 1053818881L % mod; public static long[] convolute(long[] a, long[] b, int USE, int mod) { int m = Math.max(2, Integer.highestOneBit(a.length+b.length-1)<<1); long[][] fs = new long[USE][]; for(int k = 0;k < USE;k++){ int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; long[] fa = nttmb(a, m, false, P, g, cache[k*2], k); long[] fb = a == b ? fa : nttmb(b, m, false, P, g, cache[k*2+1], k); for(int i = 0;i < m;i++){ fa[i] = fa[i]*fb[i]%P; } fs[k] = nttmb(fa, m, true, P, g, cache[k*2+1], k); } long[] res = new long[fs[0].length]; for(int i = 0;i < fs[0].length;i++){ long v0 = fs[0][i]; long v1 = (fs[1][i] - v0) * 525860363L % 1051721729L; if(v1 < 0)v1 += 1051721729L; // long temp = (v1 * 1053818881L + v0) % 1045430273L; // long v2 = (fs[2][i] - temp) * 152479290L % 1045430273L; long v2 = ((fs[2][i] + 1045430273L - v0) * 152479290L + v1 * (1045430273L-871191728L)) % 1045430273L; // if(v2 < 0)v2 += 1045430273L; long ret = (v2 * F + v1 * 1053818881L + v0) % mod; res[i] = ret; } return res; } static long[][] cache = new long[6][16384]; public static long[] convolute(long[] a, long[] b, int USE, int mod, long[][] ffb) { int m = ffb != null ? ffb[0].length : Math.max(2, Integer.highestOneBit(a.length+b.length-1)<<1); long[][] fs = new long[USE][]; for(int k = 0;k < USE;k++){ int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; long[] fa = nttmb(a, m, false, P, g, cache[k*2], k); long[] fb = ffb != null ? ffb[k] : a == b ? fa : nttmb(b, m, false, P, g, cache[k*2+1], k); for(int i = 0;i < m;i++){ // fa[i] = fa[i]*fb[i]%P; fa[i] = modh(fa[i]*fb[i], M, H, P); } fs[k] = nttmb(fa, m, true, P, g, cache[k*2+1], k); } // mods={1053818881, 1051721729, 1045430273 // gamma=[[0, 525860363, 152479290]] // tr(1053818881L * 152479290L % 1045430273L); long[] res = new long[fs[0].length]; for(int i = 0;i < fs[0].length;i++){ long v0 = fs[0][i]; long v1 = (fs[1][i] - v0) * 525860363L % 1051721729L; if(v1 < 0)v1 += 1051721729L; // long temp = (v1 * 1053818881L + v0) % 1045430273L; // long v2 = (fs[2][i] - temp) * 152479290L % 1045430273L; long v2 = ((fs[2][i] + 1045430273L - v0) * 152479290L + v1 * (1045430273L-871191728L)) % 1045430273L; // if(v2 < 0)v2 += 1045430273L; long ret = (v2 * F + v1 * 1053818881L + v0) % mod; // fs[0][i] = ret; res[i] = ret; } // for(int i = 0;i < fs[0].length;i++){ // long v0 = fs[0][i]; // long v1 = (fs[1][i] - v0) * 525860363L % 1051721729; // if(v1 < 0)v1 += 1051721729; // long temp = (v1 * 1053818881L + v0) % 1045430273L; // long v2 = (fs[2][i] - temp) * 152479290L % 1045430273L; // if(v2 < 0)v2 += 1045430273L; // long ret = ((v2 * 1051721729L + v1) % mod * 1053818881L + v0) % mod; // fs[0][i] = ret; // } return res; // return fs[0]; } static int L = 14; static int[][][] wws; static int[][][] iwws; static void superPrepare() { wws = new int[3][][]; iwws = new int[3][][]; for(int t = 0;t < 3;t++){ int P = NTTPrimes[t], g = NTTPrimitiveRoots[t]; long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; { wws[t] = new int[L+1][]; long w = (1L<<32)%P; long dw = pow(g, P-1>>>L, P); wws[t][L] = new int[1<= 1;i--){ wws[t][i] = new int[1<>>L), P); iwws[t][L] = new int[1<= 1;i--){ iwws[t][i] = new int[1<= 2*P)dst[s] -= 2*P; // long Q = (u&(1L<<32)-1)*J&(1L<<32)-1; long Q = (u<<32)*J>>>32; dst[t] = (u>>>32)-(Q*P>>>32)+P; } } } for(int i = 0;i < n;i++){ if(dst[i] >= P)dst[i] -= P; } for(int i = 0;i < n;i++){ int rev = Integer.reverse(i)>>>-h; if(i < rev){ long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if(inverse){ long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; long in = invl(n, P); for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P); } return dst; } // Modified Shoup + Barrett private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P); long[] wws = new long[1<= 2*P)ndsts -= 2*P; long T = dst[s] - dst[t] + 2*P; long Q = wws[k]*T>>>32; dst[s] = ndsts; dst[t] = ws[k]*T-Q*P&(1L<<32)-1; } } // dw = dw * dw % P; if(i < h-1){ for(int k = 0;k < 1<= P)dst[i] -= P; } for(int i = 0;i < n;i++){ int rev = Integer.reverse(i)>>>-h; if(i < rev){ long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if(inverse){ long in = invl(n, P); for(int i = 0;i < n;i++){ dst[i] = modh(dst[i] * in, M, H, P); } } return dst; } static final long mask = (1L<<31)-1; public static long modh(long a, long M, int h, int mod) { long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod; return r < mod ? r : r-mod; } private static long[] garnerPrepare(int[] m) { int n = m.length; assert n == m.length; if(n == 0)return new long[0]; long[] gamma = new long[n]; for(int k = 1;k < n;k++){ long prod = 1; for(int i = 0;i < k;i++){ prod = prod * m[i] % m[k]; } gamma[k] = invl(prod, m[k]); } return gamma; } private static long[] garnerBatch(int[] u, int[] m, long[] gamma, long[] v) { int n = u.length; assert n == m.length; // long[] v = new long[n]; v[0] = u[0]; for(int k = 1;k < n;k++){ long temp = v[k-1]; for(int j = k-2;j >= 0;j--){ temp = (temp * m[j] + v[j]) % m[k]; } v[k] = (u[k] - temp) * gamma[k] % m[k]; if(v[k] < 0)v[k] += m[k]; } return v; } private static long[] garnerBatch2(int[] u, int[] m, long[] gamma, long[] v) { int n = u.length; assert n == m.length; // long[] v = new long[n]; v[0] = u[0]; { v[1] = (u[1] - v[0]) * gamma[1] % m[1]; if(v[1] < 0)v[1] += m[1]; } { long temp = (v[1] * m[0] + v[0]) % m[2]; v[2] = (u[2] - temp) * gamma[2] % m[2]; if(v[2] < 0)v[2] += m[2]; } return v; } private static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); } public static void main(String[] args) throws Exception { new Q444_5().run(); } private byte[] inbuf = new byte[1024]; private int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }