import java.util.*; public class Main { public static void main(String[] args) throws Exception{ final ContestScanner sc = new ContestScanner(); final ContestPrinter pr = new ContestPrinter(); final ModIntFactory fact = new ModIntFactory(1_000_000_007); final ModIntFactory.ModInt A = fact.create(sc.nextLong()), B = fact.create(sc.nextLong()), C = fact.create(sc.nextLong()); final long K = sc.nextLong(); pr.println(A.mul(B,C).pow(MathLib.pow_mod(2,K, 1_000_000_007-1))); pr.close(); } } class MathLib{ private static long safe_mod(long x, long m){ x %= m; if(x<0) x += m; return x; } private static long[] inv_gcd(long a, long b){ a = safe_mod(a, b); if(a==0) return new long[]{b,0}; long s=b, t=a; long m0=0, m1=1; while(t>0){ long u = s/t; s -= t*u; m0 -= m1*u; long tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if(m0<0) m0 += b/s; return new long[]{s,m0}; } public static long gcd(long... a){ if(a.length == 0) return 0; long r = java.lang.Math.abs(a[0]); for(int i=1; i= 0; assert m >= 1; if(m == 1)return 0L; x = safe_mod(x, m); long ans = 1L; while(n > 0){ if((n&1) == 1) ans = (ans * x) % m; x = (x*x) % m; n >>>= 1; } return ans; } public static long[] crt(long[] r, long[] m){ assert(r.length == m.length); int n = r.length; long r0=0, m0=1; for(int i=0; i= m){ ans += (n-1) * n * (a/m) / 2; a %= m; } if(b >= m){ ans += n * (b/m); b %= m; } long y_max = (a*n+b) / m; long x_max = y_max * m - b; if(y_max == 0) return ans; ans += (n - (x_max+a-1)/a) * y_max; ans += floor_sum(y_max, a, m, (a-x_max%a)%a); return ans; } public static java.util.ArrayList divisors(long n){ java.util.ArrayList divisors = new ArrayList<>(); java.util.ArrayList large = new ArrayList<>(); for(long i=1; i*i<=n; i++) if(n%i==0){ divisors.add(i); if(i*i=0; p--){ divisors.add(large.get(p)); } return divisors; } } class ModIntFactory { private final ModArithmetic ma; private final int mod; private final boolean usesMontgomery; private final ModArithmetic.ModArithmeticMontgomery maMontgomery; private ArrayList factorial; public ModIntFactory(int mod) { this.ma = ModArithmetic.of(mod); this.usesMontgomery = ma instanceof ModArithmetic.ModArithmeticMontgomery; this.maMontgomery = usesMontgomery ? (ModArithmetic.ModArithmeticMontgomery) ma : null; this.mod = mod; this.factorial = new ArrayList<>(); } public ModInt create(long value) { if ((value %= mod) < 0) value += mod; if (usesMontgomery) { return new ModInt(maMontgomery.generate(value)); } else { return new ModInt((int) value); } } private void prepareFactorial(int max){ factorial.ensureCapacity(max+1); if(factorial.size()==0) factorial.add(1); if (usesMontgomery) { for(int i=factorial.size(); i<=max; i++){ factorial.add(ma.mul(factorial.get(i-1), maMontgomery.generate(i))); } } else { for(int i=factorial.size(); i<=max; i++){ factorial.add(ma.mul(factorial.get(i-1), i)); } } } public ModInt factorial(int i){ prepareFactorial(i); return create(factorial.get(i)); } public ModInt permutation(int n, int r){ if(n < 0 || r < 0 || n < r) return create(0); prepareFactorial(n); return create(ma.div(factorial.get(n), factorial.get(r))); } public ModInt combination(int n, int r){ if(n < 0 || r < 0 || n < r) return create(0); prepareFactorial(n); return create(ma.div(factorial.get(n), ma.mul(factorial.get(r),factorial.get(n-r)))); } public int getMod() { return mod; } public class ModInt { private int value; private ModInt(int value) { this.value = value; } public int mod() { return mod; } public int value() { if (usesMontgomery) { return maMontgomery.reduce(value); } return value; } public ModInt add(ModInt mi) { return new ModInt(ma.add(value, mi.value)); } public ModInt add(ModInt mi1, ModInt mi2) { return new ModInt(ma.add(value, mi1.value)).addAsg(mi2); } public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3) { return new ModInt(ma.add(value, mi1.value)).addAsg(mi2).addAsg(mi3); } public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) { return new ModInt(ma.add(value, mi1.value)).addAsg(mi2).addAsg(mi3).addAsg(mi4); } public ModInt add(ModInt mi1, ModInt... mis) { ModInt mi = add(mi1); for (ModInt m : mis) mi.addAsg(m); return mi; } public ModInt add(long mi) { return new ModInt(ma.add(value, ma.remainder(mi))); } public ModInt sub(ModInt mi) { return new ModInt(ma.sub(value, mi.value)); } public ModInt sub(long mi) { return new ModInt(ma.sub(value, ma.remainder(mi))); } public ModInt mul(ModInt mi) { return new ModInt(ma.mul(value, mi.value)); } public ModInt mul(ModInt mi1, ModInt mi2) { return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2); } public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3) { return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2).mulAsg(mi3); } public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) { return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2).mulAsg(mi3).mulAsg(mi4); } public ModInt mul(ModInt mi1, ModInt... mis) { ModInt mi = mul(mi1); for (ModInt m : mis) mi.mulAsg(m); return mi; } public ModInt mul(long mi) { return new ModInt(ma.mul(value, ma.remainder(mi))); } public ModInt div(ModInt mi) { return new ModInt(ma.div(value, mi.value)); } public ModInt div(long mi) { return new ModInt(ma.div(value, ma.remainder(mi))); } public ModInt inv() { return new ModInt(ma.inv(value)); } public ModInt pow(long b) { return new ModInt(ma.pow(value, b)); } public ModInt addAsg(ModInt mi) { this.value = ma.add(value, mi.value); return this; } public ModInt addAsg(ModInt mi1, ModInt mi2) { return addAsg(mi1).addAsg(mi2); } public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3) { return addAsg(mi1).addAsg(mi2).addAsg(mi3); } public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) { return addAsg(mi1).addAsg(mi2).addAsg(mi3).addAsg(mi4); } public ModInt addAsg(ModInt... mis) { for (ModInt m : mis) addAsg(m); return this; } public ModInt addAsg(long mi) { this.value = ma.add(value, ma.remainder(mi)); return this; } public ModInt subAsg(ModInt mi) { this.value = ma.sub(value, mi.value); return this; } public ModInt subAsg(long mi) { this.value = ma.sub(value, ma.remainder(mi)); return this; } public ModInt mulAsg(ModInt mi) { this.value = ma.mul(value, mi.value); return this; } public ModInt mulAsg(ModInt mi1, ModInt mi2) { return mulAsg(mi1).mulAsg(mi2); } public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3) { return mulAsg(mi1).mulAsg(mi2).mulAsg(mi3); } public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) { return mulAsg(mi1).mulAsg(mi2).mulAsg(mi3).mulAsg(mi4); } public ModInt mulAsg(ModInt... mis) { for (ModInt m : mis) mulAsg(m); return this; } public ModInt mulAsg(long mi) { this.value = ma.mul(value, ma.remainder(mi)); return this; } public ModInt divAsg(ModInt mi) { this.value = ma.div(value, mi.value); return this; } public ModInt divAsg(long mi) { this.value = ma.div(value, ma.remainder(mi)); return this; } @Override public String toString() { return String.valueOf(value()); } @Override public boolean equals(Object o) { if (o instanceof ModInt) { ModInt mi = (ModInt) o; return mod() == mi.mod() && value() == mi.value(); } return false; } @Override public int hashCode() { return (1 * 37 + mod()) * 37 + value(); } } private static abstract class ModArithmetic { abstract int mod(); abstract int remainder(long value); abstract int add(int a, int b); abstract int sub(int a, int b); abstract int mul(int a, int b); int div(int a, int b) { return mul(a, inv(b)); } int inv(int a) { int b = mod(); if (b == 1) return 0; long u = 1, v = 0; while (b >= 1) { int t = a / b; a -= t * b; int tmp1 = a; a = b; b = tmp1; u -= t * v; long tmp2 = u; u = v; v = tmp2; } if (a != 1) { throw new ArithmeticException("divide by zero"); } return remainder(u); } int pow(int a, long b) { if (b < 0) throw new ArithmeticException("negative power"); int r = 1; int x = a; while (b > 0) { if ((b & 1) == 1) r = mul(r, x); x = mul(x, x); b >>= 1; } return r; } static ModArithmetic of(int mod) { if (mod <= 0) { throw new IllegalArgumentException(); } else if (mod == 1) { return new ModArithmetic1(); } else if (mod == 2) { return new ModArithmetic2(); } else if (mod == 998244353) { return new ModArithmetic998244353(); } else if (mod == 1000000007) { return new ModArithmetic1000000007(); } else if ((mod & 1) == 1) { return new ModArithmeticMontgomery(mod); } else { return new ModArithmeticBarrett(mod); } } private static final class ModArithmetic1 extends ModArithmetic { int mod() {return 1;} int remainder(long value) {return 0;} int add(int a, int b) {return 0;} int sub(int a, int b) {return 0;} int mul(int a, int b) {return 0;} int pow(int a, long b) {return 0;} } private static final class ModArithmetic2 extends ModArithmetic { int mod() {return 2;} int remainder(long value) {return (int) (value & 1);} int add(int a, int b) {return a ^ b;} int sub(int a, int b) {return a ^ b;} int mul(int a, int b) {return a & b;} } private static final class ModArithmetic998244353 extends ModArithmetic { private final int mod = 998244353; int mod() { return mod; } int remainder(long value) { return (int) ((value %= mod) < 0 ? value + mod : value); } int add(int a, int b) { int res = a + b; return res >= mod ? res - mod : res; } int sub(int a, int b) { int res = a - b; return res < 0 ? res + mod : res; } int mul(int a, int b) { return (int) (((long) a * b) % mod); } } private static final class ModArithmetic1000000007 extends ModArithmetic { private final int mod = 1000000007; int mod() { return mod; } int remainder(long value) { return (int) ((value %= mod) < 0 ? value + mod : value); } int add(int a, int b) { int res = a + b; return res >= mod ? res - mod : res; } int sub(int a, int b) { int res = a - b; return res < 0 ? res + mod : res; } int mul(int a, int b) { return (int) (((long) a * b) % mod); } } private static final class ModArithmeticMontgomery extends ModArithmeticDynamic { private final long negInv; private final long r2; private ModArithmeticMontgomery(int mod) { super(mod); long inv = 0; long s = 1, t = 0; for (int i = 0; i < 32; i++) { if ((t & 1) == 0) { t += mod; inv += s; } t >>= 1; s <<= 1; } long r = (1l << 32) % mod; this.negInv = inv; this.r2 = (r * r) % mod; } private int generate(long x) { return reduce(x * r2); } private int reduce(long x) { x = (x + ((x * negInv) & 0xffff_ffffl) * mod) >>> 32; return (int) (x < mod ? x : x - mod); } @Override int remainder(long value) { return generate((value %= mod) < 0 ? value + mod : value); } @Override int mul(int a, int b) { return reduce((long) a * b); } @Override int inv(int a) { return super.inv(reduce(a)); } @Override int pow(int a, long b) { return generate(super.pow(a, b)); } } private static final class ModArithmeticBarrett extends ModArithmeticDynamic { private static final long mask = 0xffff_ffffl; private final long mh; private final long ml; private ModArithmeticBarrett(int mod) { super(mod); /** * m = floor(2^64/mod) * 2^64 = p*mod + q, 2^32 = a*mod + b * => (a*mod + b)^2 = p*mod + q * => p = mod*a^2 + 2ab + floor(b^2/mod) */ long a = (1l << 32) / mod; long b = (1l << 32) % mod; long m = a * a * mod + 2 * a * b + (b * b) / mod; mh = m >>> 32; ml = m & mask; } private int reduce(long x) { long z = (x & mask) * ml; z = (x & mask) * mh + (x >>> 32) * ml + (z >>> 32); z = (x >>> 32) * mh + (z >>> 32); x -= z * mod; return (int) (x < mod ? x : x - mod); } @Override int remainder(long value) { return (int) ((value %= mod) < 0 ? value + mod : value); } @Override int mul(int a, int b) { return reduce((long) a * b); } } private static class ModArithmeticDynamic extends ModArithmetic { final int mod; ModArithmeticDynamic(int mod) { this.mod = mod; } int mod() { return mod; } int remainder(long value) { return (int) ((value %= mod) < 0 ? value + mod : value); } int add(int a, int b) { int sum = a + b; return sum >= mod ? sum - mod : sum; } int sub(int a, int b) { int sum = a - b; return sum < 0 ? sum + mod : sum; } int mul(int a, int b) { return (int) (((long) a * b) % mod); } } } } class ContestScanner { private final java.io.InputStream in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int buflen = 0; private static final long LONG_MAX_TENTHS = 922337203685477580L; private static final int LONG_MAX_LAST_DIGIT = 7; private static final int LONG_MIN_LAST_DIGIT = 8; public ContestScanner(java.io.InputStream in){ this.in = in; } public ContestScanner(){ this(System.in); } private boolean hasNextByte() { if (ptr < buflen) { return true; }else{ ptr = 0; try { buflen = in.read(buffer); } catch (java.io.IOException e) { e.printStackTrace(); } if (buflen <= 0) { return false; } } return true; } private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1; } private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126; } public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte(); } public String next() { if (!hasNext()) throw new java.util.NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while(isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } public long nextLong() { if (!hasNext()) throw new java.util.NoSuchElementException(); long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } if (b < '0' || '9' < b) { throw new NumberFormatException(); } while (true) { if ('0' <= b && b <= '9') { int digit = b - '0'; if (n >= LONG_MAX_TENTHS) { if (n == LONG_MAX_TENTHS) { if (minus) { if (digit <= LONG_MIN_LAST_DIGIT) { n = -n * 10 - digit; b = readByte(); if (!isPrintableChar(b)) { return n; } else if (b < '0' || '9' < b) { throw new NumberFormatException( String.format("%d%s... is not number", n, Character.toString(b)) ); } } } else { if (digit <= LONG_MAX_LAST_DIGIT) { n = n * 10 + digit; b = readByte(); if (!isPrintableChar(b)) { return n; } else if (b < '0' || '9' < b) { throw new NumberFormatException( String.format("%d%s... is not number", n, Character.toString(b)) ); } } } } throw new ArithmeticException( String.format("%s%d%d... overflows long.", minus ? "-" : "", n, digit) ); } n = n * 10 + digit; }else if(b == -1 || !isPrintableChar(b)){ return minus ? -n : n; }else{ throw new NumberFormatException(); } b = readByte(); } } public int nextInt() { long nl = nextLong(); if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException(); return (int) nl; } public double nextDouble() { return Double.parseDouble(next()); } public long[] nextLongArray(int length){ long[] array = new long[length]; for(int i=0; i