module AtCoder


open Microsoft.FSharp.Collections
open System
open System.Collections
open System.Collections.Generic

#nowarn "0025" // パターンマッチが不完全である警告の無効

module Seq =
    let interval startInclusive endExclusive = seq { startInclusive .. (endExclusive - 1) }

    let inline mapAdjacent (op: 'a -> 'a -> 'b) (source: seq<'a>): seq<'b> =
        match source with
        | source when Seq.isEmpty source -> Seq.empty
        | _ -> Seq.map2 op source (Seq.tail source)

module Array2D =
    let inline transpose (array: 'a [,]): 'a [,] =
        let transposed = Array2D.zeroCreate (Array2D.length2 array) (Array2D.length1 array)
        transposed |> Array2D.mapi (fun i k _ -> array.[k, i])


module InputOutputs =
    let read(): string = Console.ReadLine()
    let reads(): string [] = read().Split()

    let readMatrix (rowNum: int32): string [,] =
        let mutable lines = Array.zeroCreate rowNum
        for i in Seq.interval 0 rowNum do
            lines.[i] <- reads()

        lines |> array2D


    let readInt32(): int32 = read() |> int32
    let readInt64(): int64 = read() |> int64
    let readInt32s(): int32 [] = reads() |> Array.map int32
    let readInt64s(): int64 [] = reads() |> Array.map int64

    let readMatrixInt32 (rowNum: int32): int32 [,] = readMatrix rowNum |> Array2D.map int32

    let readMatrixInt64 (rowNum: int32): int64 [,] = readMatrix rowNum |> Array2D.map int64

    let inline print (item: 'a): unit = printfn "%s" (string item)

    let inline printRow (line: seq<'a>): unit =
        let strs = line |> Seq.map string
        if not (Seq.isEmpty strs) then
            printf "%s" (Seq.head strs)
            for s in Seq.skip 1 strs do
                printf " %s" s
        printf "\n"

    let inline printColumn (line: seq<'a>): unit =
        for item in line do
            print item

    let inline printGridGraph (lines: 'a [,]): unit =
        for i in (Seq.interval 0 lines.Length) do
            lines.[i, *]
            |> Seq.map string
            |> String.concat " "
            |> print

module NumericFunctions =
    type Mods =
        { divisor: int32 }

        member this.Mod(a: int64) =
            let b = a % int64 this.divisor |> int32
            if b < 0 then b + this.divisor
            else b

        member this.Mod(a: int32) = this.Mod(int64 a)
        member this.Add (a: int32) (b: int32): int32 = (this.Mod a + this.Mod b) % this.divisor

        member this.Sub (a: int32) (b: int32): int32 =
            let sub = (this.Mod a - this.Mod b) % this.divisor
            if sub < 0 then sub + this.divisor
            else sub

        member this.Mul (a: int32) (b: int32): int32 =
            (int64 (this.Mod a) * int64 (this.Mod b)) % int64 this.divisor |> int32

        /// 二分累積 O(Log N)
        member this.Pow (b: int32) (n: int32): int32 =
            let digit = int32 (Math.Log(float n, 2.0))

            let seqs =
                seq { 0 .. digit }
                |> Seq.scan (fun acm _ -> this.Mul acm acm) b
                |> Seq.toArray
            seq { 0 .. digit }
            |> Seq.fold (fun acm i ->
                if ((n >>> i) &&& 1) = 1 then this.Mul acm seqs.[i]
                else acm) 1

        /// フェルマーの小定理より
        member this.Inv(a: int32): int32 = this.Pow a (this.divisor - 2)

        member this.Div (a: int32) (b: int32): int32 = this.Mul a (this.Inv b)

        member this.Perm (n: int32) (k: int32): int32 =
            match (n, k) with
            | (n, _) when n < 0 -> invalidArg "n" "n >= 0"
            | (_, k) when k < 0 -> invalidArg "k" "k >= 0"
            | (n, k) when k > n -> 0
            | _ -> seq { n - k + 1 .. n } |> Seq.fold this.Mul 1

        member this.FactTable(nMax: int32): int32 [] =
            seq { 1 .. nMax }
            |> Seq.scan this.Mul 1
            |> Seq.toArray

        /// パスカルの三角形 O(N^2)
        member this.CombTable(nMax: int32): int32 [,] =
            let table = Array2D.zeroCreate (nMax + 1) (nMax + 1)
            for n in 0 .. nMax do
                for k in 0 .. nMax do
                    match (n, k) with
                    | (n, k) when n < k -> table.[n, k] <- 0
                    | (_, k) when k = 0 -> table.[n, k] <- 1
                    | _ ->
                        table.[n, k] <- int64 table.[n - 1, k - 1] + int64 table.[n - 1, k] % int64 this.divisor
                                        |> int32
            table

    let isEven (a: int64): bool = a % 2L = 0L
    let isOdd (a: int64): bool = not (isEven a)

    /// ユークリッドの互除法 O(Log N)
    let rec gcd (m: int64) (n: int64): int64 =
        match (m, n) with
        | (m, _) when m <= 0L -> invalidArg "m" "m <= 0"
        | (_, n) when n <= 0L -> invalidArg "n" "n <= 0"
        | (m, n) when m < n -> gcd n m
        | (m, n) when m % n = 0L -> n
        | _ -> gcd n (m % n)

    /// gcdを使っているため O(Log N)
    let lcm (m: int64) (n: int64): int64 = (bigint m) * (bigint n) / bigint (gcd m n) |> Checked.int64

    /// O(√N)
    let divisors (m: int64): seq<int64> =
        match m with
        | m when m <= 0L -> invalidArg "m" "m <= 0"
        | _ ->
            let sqrtM = int (sqrt (float m))

            let overRootM =
                Seq.interval 1 (sqrtM + 1)
                |> Seq.map int64
                |> Seq.filter (fun d -> m % d = 0L)
                |> Seq.rev
            overRootM
            |> if int64 sqrtM * int64 sqrtM = m then Seq.tail
               else id
            |> Seq.map (fun x -> m / x)
            |> Seq.append overRootM

    /// O(√N)
    let rec commonDivisor (m: int64) (n: int64): seq<int64> =
        match (m, n) with
        | (_, n) when n <= 0L -> invalidArg "n" "n <= 0"
        | (m, n) when m < n -> commonDivisor n m
        | _ -> divisors n |> Seq.filter (fun nd -> m % nd = 0L)

    /// エラトステネスの篩 O(N loglog N)
    let primes (n: int32): seq<int32> =
        match n with
        | n when n <= 1 -> invalidArg "n" "n <= 1"
        | _ ->
            let sqrtN = int32 (sqrt (float n))
            let mutable sieve = Seq.interval 2 (n + 1) |> Seq.toList
            let mutable ps = []
            while not (List.isEmpty sieve) && List.head sieve <= sqrtN do
                let m = List.head sieve
                ps <- m :: ps
                sieve <- List.filter (fun p -> p % m <> 0) sieve
            List.append ps sieve |> Seq.ofList

    /// 試し割り法 O(√N)
    let primeFactrization (n: int64): seq<int64 * int64> =
        match n with
        | n when n <= 1L -> invalidArg "n" "n <= 1"
        | _ ->
            let mutable i = 2L
            let mutable m = n
            let mutable ps = []
            while i * i <= n do
                if m % i = 0L then
                    let mutable count = 0L
                    while m % i = 0L do
                        count <- count + 1L
                        m <- m / i
                    ps <- (int64 i, count) :: ps
                i <- i + 1L
            if m <> 1L then ps <- (m, 1L) :: ps
            List.toSeq ps

module Algorithm =
    let rec binarySearch (predicate: int64 -> bool) (ng: int64) (ok: int64): int64 =
        match (ok, ng) with
        | (ok, ng) when abs (ok - ng) = 1L -> ok
        | _ ->
            let mid = (ok + ng) / 2L
            if predicate mid then binarySearch predicate ng mid
            else binarySearch predicate mid ok

    let leftBinarySearch (size: int64) (predicate: int64 -> bool): int64 option =
        binarySearch predicate size -1L
        |> fun ix ->
            if ix = -1L then None
            else Some ix

    let rightBinarySearch (size: int64) (predicate: int64 -> bool): int64 option =
        binarySearch predicate -1L size
        |> fun ix ->
            if ix = size then None
            else Some ix

    let runLengthEncoding (source: string): seq<string * int32> =
        match source.Length with
        | n when n = 0 -> Seq.empty
        | n ->
            let cutIxs = Seq.interval 1 n |> Seq.filter (fun i -> source.[i] <> source.[i - 1])
            Seq.append (Seq.append (seq { yield 0 }) cutIxs) (seq { yield n })
            |> Seq.mapAdjacent (fun i0 i1 -> (string source.[i0], i1 - i0))

    let rec ternarySearchDownward (left: float) (right: float) (convexFunction: float -> float) (allowableError: float) =
        match left, right, convexFunction, allowableError with
        | l, r, f, e when r - l < e -> l
        | l, r, f, e ->
            let ml = l + (r - l) / 3.0
            let mr = l + (r - l) / 3.0 * 2.0
            if f ml < f mr then ternarySearchDownward l mr f e
            else if f ml > f mr then ternarySearchDownward ml r f e
            else ternarySearchDownward ml mr f e

    let rec ternarySearchUpward (left: float) (right: float) (convexFunction: float -> float) (allowableError: float) =
        match left, right, convexFunction, allowableError with
        | l, r, f, e when r - l < e -> l
        | l, r, f, e ->
            let ml = l + (r - l) / 3.0
            let mr = l + (r - l) / 3.0 * 2.0
            if f ml < f mr then ternarySearchUpward ml r f e
            else if f ml > f mr then ternarySearchUpward l mr f e
            else ternarySearchUpward ml mr f e

    let checkFlag (flag : int) (flagNumber : int) : bool =
        if (flag < 0) then invalidArg "flag" "flag < 0"
        if (flagNumber < 0) then invalidArg "flagNumber" "flagNumber < 0"
        flag >>> flagNumber &&& 1 = 1

module DataStructure =
    module UnionFind =
        type private Id = Int32

        type UnionFind(n) =
            let mutable parent: Id [] = Array.init n id
            let mutable size: int32 [] = Array.create n 1

            let rec root u =
                if parent.[u] = u then
                    u
                else
                    let rootParent = root parent.[u]
                    parent.[u] <- rootParent
                    rootParent

            member this.Unite (u: Id) (v: Id): unit =
                if root u = root v then
                    ()
                else
                    parent.[root u] <- root v
                    size.[root v] <- size.[root u] + size.[root v]

            member this.Size(u: Id): int32 = size.[root u]

            member this.Find (u: Id) (v: Id): bool = root u = root v

            member this.Root (u: int32) : Id = root u

    let reverseCompare (x: 'a) (y: 'a): int32 = compare x y * -1

    module PriorityQueue =
        type PriorityQueue<'a when 'a: comparison and 'a: equality>(values: seq<'a>, comparison: 'a -> 'a -> int32) =

            let dict =
                let sorted = SortedDictionary<'a, Queue<'a>>(ComparisonIdentity.FromFunction comparison)
                Seq.groupBy id values |> Seq.iter (fun (key, value) -> sorted.Add(key, (new Queue<'a>(value))))
                sorted

            let mutable size = dict.Count
            new(values: seq<'a>) = PriorityQueue(values, compare)

            member this.Enqueue(item: 'a): unit =
                if dict.ContainsKey item then
                    dict.[item].Enqueue(item)
                else
                    let added = new Queue<'a>()
                    added.Enqueue(item)
                    dict.Add(item, added)
                size <- size + 1

            member this.Peek =
                if Seq.isEmpty dict then invalidOp "queue is Empty"

                (Seq.head dict).Value |> Seq.head

            member this.Size = size

            member this.Dequeue(): 'a =
                if Seq.isEmpty dict then invalidOp "queue is Empty"

                let first = Seq.head dict
                if first.Value.Count <= 1 then dict.Remove(first.Key) |> ignore

                size <- size - 1
                first.Value.Dequeue()

            interface IEnumerable<IEnumerable<'a>> with
                member this.GetEnumerator() =
                    (seq {
                        for kv in dict -> seq kv.Value
                     }).GetEnumerator()

            interface IEnumerable with
                member this.GetEnumerator() = (this :> IEnumerable<IEnumerable<'a>>).GetEnumerator() :> IEnumerator


open Algorithm
open DataStructure
open InputOutputs
open NumericFunctions

[<EntryPoint>]
let main _ =
    let [|N;M;K|] = readInt32s ()

    let mods = {Mods.divisor = 1000000007}
    let sumX =
        Seq.interval 1 M
        |> Seq.fold (fun state d ->
            mods.Add state (mods.Mul (mods.Mul (mods.Mul d (M - d)) N) N))
            0
        |> (fun x ->
            let c = mods.Div (mods.Perm (N * M - 2) (K - 2)) (mods.Perm (K-2) (K-2))
            mods.Mul x c)
    let sumY =
        Seq.interval 1 N
        |> Seq.fold (fun state d ->
            mods.Add state (mods.Mul (mods.Mul (mods.Mul d (N - d)) M) M))
            0
        |> (fun y ->
            let c = mods.Div (mods.Perm (N * M - 2) (K - 2)) (mods.Perm (K-2) (K-2))
            mods.Mul y c)
    let ans = mods.Add sumX sumY
    print ans
    0 // return an integer exit code


Measured memory_bytes: 14288