package q5xx; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.HashMap; import java.util.InputMismatchException; import java.util.Map; public class Q561_2 { InputStream is; PrintWriter out; String INPUT = ""; // 10^9:1344 // 2^31:1600 int[] divs(int n) { int[] high = new int[1344]; int[] low = new int[1344]; int p = 0, q = 0; for(int i = 1;i*i <= n;i++){ if(n % i == 0){ low[p++] = i; if(i*i < n)high[q++] = n/i; } } while(q-1 >= 0){ low[p++] = high[q-1]; q--; } return Arrays.copyOf(low, p); } void solve() { int h = ni(), w = ni(), K = ni(); int[] dhs = divs(h); int[] dws = divs(w); int mod = 1000000007; int[] numhs = new int[dhs.length]; for(int i = dhs.length-1;i >= 0;i--){ numhs[i] = h/dhs[i]; for(int j = i+1;j < dhs.length;j++){ if(dhs[j] % dhs[i] == 0){ numhs[i] -= numhs[j]; } } } int[] numws = new int[dws.length]; for(int i = dws.length-1;i >= 0;i--){ numws[i] = w/dws[i]; for(int j = i+1;j < dws.length;j++){ if(dws[j] % dws[i] == 0){ numws[i] -= numws[j]; } } } long ret = 0; long big = 8L*mod*mod; for(int i = 0;i < dhs.length;i++){ for(int j = 0;j < dws.length;j++){ long x = h/dhs[i]; long y = w/dws[j]; long z = x*(y/gcd(x,y)); long key = (long)h*w/z; if(!cache.containsKey(key)){ cache.put(key, pow(K, (long)h*w/z, mod)); } ret += cache.get(key) * numhs[i] % mod * numws[j]; if(ret >= big)ret -= big; } } ret = ret % mod * invl(h, mod) % mod * invl(w, mod) % mod; out.println(ret); } static Map cache = new HashMap<>(); public static long gcd(long a, long b) { while (b > 0) { long 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; } 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 Q561_2().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)); } }