public static void Solve()
{
var(N, M, K) = Scanner.Scan <long, long, long>();
const long p = (long)1e9 + 7;
var all = N * M;
var cx = N * N % p;
cx *= Enumeration.CombinationCount(all - 2, K - 2, p);
cx %= p;
var nx = 0L;
for (var i = 1; i < M; i++)
{
nx = (nx + i * (M - i) % p) % p;
}
nx = nx * cx % p;
var cy = M * M % p;
cy *= Enumeration.CombinationCount(all - 2, K - 2, p);
cy %= p;
var ny = 0L;
for (var i = 1; i < N; i++)
{
ny = (ny + i * (N - i) % p) % p;
}
ny = ny * cy % p;
var answer = (nx + ny) % p;
Console.WriteLine(answer);
}
public static void Solve()
{
var(W, H) = Scanner.Scan <int, int>();
var p = (int)1e9 + 7;
Console.WriteLine(Enumeration.CombinationCount(W + H - 2, W - 1, p));
}
public static void Solve()
{
var N = Scanner.Scan <int>();
const int max = (int)1e5 + 1;
const int p = 998244353;
var G = new ModuloInteger[max];
G[0] = 1;
for (var i = 1; i < max; i++)
{
G[i] = G[i - 1] * (2 * i - 1);
}
var freq = new int[max];
for (var i = 0; i < 2 * N; i++)
{
var H = Scanner.Scan <int>();
freq[H]++;
}
var queue = new Queue <ModuloInteger[]>();
queue.Enqueue(new ModuloInteger[] { 1 });
foreach (var n in freq)
{
if (n < 2)
{
continue;
}
var list = new ModuloInteger[n / 2 + 1];
for (var i = 0; i * 2 <= n; i++)
{
list[i] = Enumeration.CombinationCount(n, i * 2, p) * G[i];
if (i % 2 == 1)
{
list[i] = -list[i];
}
}
queue.Enqueue(list);
}
while (queue.Count > 1)
{
var list1 = queue.Dequeue();
var list2 = queue.Dequeue();
queue.Enqueue(Convolution.Execute(list1, list2).ToArray());
}
ModuloInteger answer = 0;
var last = queue.Dequeue();
for (var i = 0; i < last.Length; i++)
{
answer += last[i] * G[N - i];
}
Console.WriteLine(answer);
}
public static void Solve()
{
var(N, M) = Scanner.Scan <int, int>();
const int p = (int)1e9 + 7;
var answer = Enumeration.PermutationCount(M, N, p);
for (var i = 1; i <= N; i++)
{
var tmp = Enumeration.CombinationCount(N, i, p) * Enumeration.PermutationCount(M - i, N - i, p);
if (i % 2 == 0)
{
answer += tmp;
}
else
{
answer -= tmp;
}
if (answer < 0)
{
answer += p;
}
answer %= p;
}
answer *= Enumeration.PermutationCount(M, N, p);
answer %= p;
Console.WriteLine(answer);
}
public static void Solve()
{
var N = Scanner.Scan <int>();
var K = Scanner.Scan <int>();
var p = (int)1e9 + 7;
var answer = Enumeration.CombinationCount(N - 1 + K, N - 1, p);
Console.WriteLine(answer);
}
public static void Solve()
{
var(N, K) = Scanner.Scan <int, int>();
const int p = (int)1e9 + 7;
for (var i = 1; i <= K; i++)
{
var a = Enumeration.CombinationCount(N - K + 1, i, p);
var b = Enumeration.CombinationCount(K - 1, i - 1, p);
Console.WriteLine(a * b % p);
}
}
public static void Solve()
{
var(R, C) = Scanner.Scan <long, long>();
var(X, Y) = Scanner.Scan <long, long>();
var(D, L) = Scanner.Scan <long, long>();
var p = (int)1e9 + 7;
long Calc(long x, long y, long d, long l, long mod)
{
if (x * y < d + l)
{
return(0);
}
var ret = Enumeration.CombinationCount(x * y, d, mod);
ret *= Enumeration.CombinationCount(x * y - d, l, mod);
ret %= mod;
return(ret);
}
var pattern = ((R - X + 1) * (C - Y + 1)) % p;
var comb = 0L;
if (D + L == X * Y)
{
comb = Enumeration.CombinationCount(D + L, D, p);
}
else
{
comb = Calc(X, Y, D, L, p);
comb = (comb + p - (Calc(X - 1, Y, D, L, p) * 2) % p) % p;
comb = (comb + p - (Calc(X, Y - 1, D, L, p) * 2) % p) % p;
comb = (comb + (Calc(X - 1, Y - 1, D, L, p) * 4) % p) % p;
comb = (comb + Calc(X - 2, Y, D, L, p)) % p;
comb = (comb + Calc(X, Y - 2, D, L, p)) % p;
comb = (comb + p - (Calc(X - 2, Y - 1, D, L, p) * 2) % p) % p;
comb = (comb + p - (Calc(X - 1, Y - 2, D, L, p) * 2) % p) % p;
comb = (comb + Calc(X - 2, Y - 2, D, L, p)) % p;
}
var answer = (comb * pattern) % p;
Console.WriteLine(answer);
}
public static void Solve()
{
var HWAB = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
var(H, W, A, B) = (HWAB[0], HWAB[1], HWAB[2], HWAB[3]);
var p = (long)1e9 + 7;
var answer = 0L;
for (var i = 0; i < H - A; i++)
{
var way1 = Enumeration.CombinationCount(i + B - 1, B - 1, p);
var way2 = Enumeration.CombinationCount(H - i - 1 + W - B - 1, W - B - 1, p);
answer += (way1 * way2) % p;
answer %= p;
}
Console.WriteLine(answer);
}
public static void Solve()
{
var(N, M, K) = Scanner.Scan <int, int, int>();
const long p = 998244353;
var answer = 0L;
for (var k = 0; k <= K; k++)
{
var comb = M * Enumeration.CombinationCount(N - 1, k, p);
comb %= p;
comb *= Enumeration.Power(M - 1, N - 1 - k, p);
comb %= p;
answer += comb;
answer %= p;
}
Console.WriteLine(answer);
}
public static void Solve()
{
var(X, Y) = Scanner.Scan <int, int>();
const int p = (int)1e9 + 7;
var step = (X + Y);
if ((step % 3) != 0)
{
Console.WriteLine(0); return;
}
var nm = step / 3;
var n = X - nm;
var m = Y - nm;
if (n < 0 || m < 0)
{
Console.WriteLine(0); return;
}
Console.WriteLine(Enumeration.CombinationCount(n + m, n, p));
}
public static void Solve()
{
var(N, K) = Scanner.Scan <int, int>();
var A = Scanner.ScanEnumerable <int>().ToArray();
var p = (int)1e9 + 7;
Array.Sort(A);
var answer = 0L;
for (var i = 0; i <= N - K; i++)
{
answer += (-A[i] * Enumeration.CombinationCount(N - i - 1, K - 1, p) + p) % p;
answer %= p;
}
for (var i = K - 1; i < N; i++)
{
answer += A[i] * Enumeration.CombinationCount(i, K - 1, p) % p;
answer %= p;
}
Console.WriteLine(answer);
}
