import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, 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.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(uint M_) { import std.conv : to; alias M = M_; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = x_ % M; } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } enum MO = 10^^9 + 7; alias Mint = ModInt!MO; enum LIM = 2 * 10^^5 + 10; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM]; fac = new Mint[LIM]; invFac = new Mint[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]); } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (n < 0) { if (k >= 0) { return (-1)^^(k & 1) * binom(-n + k - 1, k); } else if (n - k >= 0) { return (-1)^^((n - k) & 1) * binom(-k - 1, n - k); } else { return Mint(0); } } else { if (0 <= k && k <= n) { assert(n < LIM); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } } Mint[2][2] mul(Mint[2][2] a, Mint[2][2] b) { Mint[2][2] c; static foreach (i; 0 .. 2) static foreach (k; 0 .. 2) static foreach (j; 0 .. 2) { c[i][j] += a[i][k] * b[k][j]; } return c; } Mint[2][2] power(Mint[2][2] a, long e) { Mint[2][2] x = a, y; y[0][0] = y[1][1] = 1; for (; e; e >>= 1) { if (e & 1) y = mul(y, x); x = mul(x, x); } return y; } void main() { prepare; // 010, 012 int[6 + 1][2][2] cnt; { int[3] bs; void dfs(int s, int pos, int k) { if (pos == 3) { const a2 = [0, 2][s]; bool ok = true; ok = ok && (0 != bs[0]); ok = ok && (1 != bs[1]); ok = ok && (a2 != bs[2]); ok = ok && (bs[0] != bs[1]); ok = ok && (bs[1] != bs[2]); if (ok) { ++cnt[s][(bs[0] == bs[2]) ? 0 : 1][k]; } } else { foreach (b; 0 .. k + 1) { bs[pos] = b; dfs(s, pos + 1, (b == k) ? (k + 1) : k); } } } dfs(0, 0, 2); dfs(1, 0, 3); } debug { writeln("cnt = ", cnt); } try { for (; ; ) { const N = readInt; const M = readLong; const K = readInt; Mint calc(Mint k) { Mint ret; final switch (N) { case 1: { ret = k * (k - 1)^^(M - 1); } break; case 2: { Mint num; // 01 -> 10 num += 1; // 01 -> 12, 20 num += 2 * (k - 2); // 01 -> 23 num += (k - 2) * (k - 3); ret = k * (k - 1) * num^^(M - 1); } break; case 3: { Mint[2][2] a; foreach (i; 0 .. 2) foreach (j; 0 .. 2) { Mint num = 1; foreach (l; [2, 3][i] .. 6 + 1) { a[i][j] += cnt[i][j][l] * num; num *= (k - l); } } const aa = a.power(M - 1); ret += k * (k - 1) * (aa[0][0] + aa[0][1]); ret += k * (k - 1) * (k - 2) * (aa[1][0] + aa[1][1]); } break; } return ret; } Mint ans; foreach (k; 0 .. K + 1) { ans += (-1)^^(k & 1) * binom(K, k) * calc(Mint(K - k)); } writeln(ans); } } catch (EOFException e) { } }