package contest200501; 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 E { InputStream is; PrintWriter out; String INPUT = ""; void solve() { // a[i]=0*M or 1*N // a[i+1]^a[i] = 0を満たす組がK個以上 // ABcd // // 01:A, 10:B, 00:C, 11:D // A=B, B+D=M, A+C=N // C+D >= K int mod = 1000000007; int[][] fif = enumFIF(500000, mod); int n = ni(), m = ni(), K = ni(); long ans = 0; for(int A = 1;A <= n && A <= m;A++) { int D = m-A, C = n-A; if(D >= 0 && C >= 0 && C+D >= K) { long V = C(C+A-1+1, A-1+1, mod, fif) * C(D+A-1, A-1, mod, fif) % mod * fif[0][n-1] % mod * fif[0][m] % mod; ans += V; } } out.println(ans%mod); } public static int gcd(int a, int b) { while (b > 0) { int c = a; a = b; b = c % b; } return a; } 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 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; } public static int[] enumDivisorsFast(int n, int[] lpf) { int[] divs = {1}; while(lpf[n] > 0){ int p = lpf[n]; int e = 0; for(;p == lpf[n];e++, n /= p); int olen = divs.length; divs = Arrays.copyOf(divs, olen*(e+1)); for(int i = olen;i < divs.length;i++)divs[i] = divs[i-olen] * p; } return divs; } public static long C(int n, int r, int mod, int[][] fif) { if (n < 0 || r < 0 || r > n) return 0; return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod; } public static int[] enumLowestPrimeFactors(int n) { int tot = 0; int[] lpf = new int[n + 1]; int u = n + 32; double lu = Math.log(u); int[] primes = new int[(int) (u / lu + u / lu / lu * 1.5)]; for (int i = 2; i <= n; i++) lpf[i] = i; for (int p = 2; p <= n; p++) { if (lpf[p] == p) primes[tot++] = p; int tmp; for (int i = 0; i < tot && primes[i] <= lpf[p] && (tmp = primes[i] * p) <= n; i++) { lpf[tmp] = primes[i]; } } return lpf; } public static int[][] enumFIF(int n, int mod) { int[] f = new int[n + 1]; int[] invf = new int[n + 1]; f[0] = 1; for (int i = 1; i <= n; i++) { f[i] = (int) ((long) f[i - 1] * i % mod); } long a = f[n]; 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; } invf[n] = (int) (p < 0 ? p + mod : p); for (int i = n - 1; i >= 0; i--) { invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod); } return new int[][] { f, invf }; } 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"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new E().run(); } private byte[] inbuf = new byte[1024]; public 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 int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } 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[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } 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)); } }