Let \(f(h,w)\) be the number of ways to place K cells in a \(h\times w\) grid such that the minimal rectangle required to enclose all of them is the whole grid. This is simply the number of ways to place K cells in a \(h\times w\) grid minus the number of ways to place K cells on all sub-rectangles of size \(h'\times w'\) for \(h'<h\) or \(w'<w\) such that the corresponding smaller sub-rectangle is the minimal enclosing rectangle.

There are \((h-h'+1)(w-w'+1)\) such sub-rectangles for any size \(h'\times w'\). Using this we may formulate the recursion:

\( f(h,w)=\binom{hw}{K}-\sum_{(h'<h) \lor (w'<w)} (h-h'+1)(w-w'+1)f(h',w') \)

There are four terms in this summation:

• \(C_0(h,w)=\sum_{h',w'} f(h',w') \)
• \(C_1(h,w)=\sum_{h',w'} w'f(h',w') \)
• \(C_2(h,w)=\sum_{h',w'} h'f(h',w') \)
• \(C_3(h'w)=\sum_{h',w'} h'w'f(h',w') \) each of which can be suitably computed using the standard 2D cumulative sum approach. Finally \(f(h,w)\) is given as

\(f(h,w)=\binom{hw}{K}-(h+1)(w+1)C_0(h,w)+(h+1)C_1(h,w)+(w+1)C_2(h,w)-C_3(h,w)\).

Thus the total number of ways to enclose \(K\) cells within a grid of size \(h\times w\) in the original rectangle is

\((H-h+1)(W-w+1)f(h,w)\). Then the expected area becomes

\(E(H,W,K)=\frac{1}{\binom{HW}{K}} \sum_{h\leq H} \sum_{w \leq W} (H-h+1)(W-w+1)f(h,w) \times hw\)

#include<bits/stdc++.h>
#define MAXN 1000
#define MODD 998244353
#define ll long long
using namespace std;

ll fact[MAXN*MAXN+2];
ll factinv[MAXN*MAXN+2];
ll modpow(ll x, ll y) {
    ll xs = x;
    ll answer = 1;
    while(y) {
        if (y&1) {
            answer = (answer * xs) % MODD;
        }
        y >>= 1;
        xs = (xs * xs) % MODD ;
    }
    return answer;
}

ll B(ll x, ll y) {
	if (x < y) return 0;
	if (y == 0) return 1;
	return fact[x]*factinv[y]%MODD*factinv[x-y]%MODD;
}

ll ways[MAXN+1][MAXN+1];
ll C[4][MAXN+1][MAXN+1];
int main() {
	int H,W,K;
	cin>>H>>W>>K;
	fact[0]=factinv[0]=1;
	for(int i=1;i<=H*W;i++) {
		fact[i]=(fact[i-1]*i)%MODD;
		factinv[i]=modpow(fact[i],MODD-2);
	}
	ll ans=0;
	for(int h=1;h<=H;h++) {
		for(int w=1;w<=W;w++) {	
			ll ways_to_enclose_smaller=0;
			ways_to_enclose_smaller += (h+1)*(w+1)*(C[0][h-1][w]+C[0][h][w-1]-C[0][h-1][w-1]);
			ways_to_enclose_smaller -= (h+1)*(C[1][h-1][w]+C[1][h][w-1]-C[1][h-1][w-1]);
			ways_to_enclose_smaller -= (w+1)*(C[2][h-1][w]+C[2][h][w-1]-C[2][h-1][w-1]);
			ways_to_enclose_smaller += (C[3][h-1][w]+C[3][h][w-1]-C[3][h-1][w-1]);
			ways_to_enclose_smaller %= MODD;
			ways[h][w]=B(h*w,K)-ways_to_enclose_smaller;
			ways[h][w]%=MODD;
			if (ways[h][w]<0)ways[h][w]+=MODD;
			ans += h*w*(H-h+1ll)*(W-w+1ll)%MODD*ways[h][w]%MODD;
			ans %= MODD;
			C[0][h][w]=ways[h][w]+C[0][h-1][w]+C[0][h][w-1]-C[0][h-1][w-1];
			C[1][h][w]=w*ways[h][w]+C[1][h-1][w]+C[1][h][w-1]-C[1][h-1][w-1];
			C[2][h][w]=h*ways[h][w]+C[2][h-1][w]+C[2][h][w-1]-C[2][h-1][w-1];
			C[3][h][w]=w*h*ways[h][w]+C[3][h-1][w]+C[3][h][w-1]-C[3][h-1][w-1];
			for(int j=0;j<4;j++) {
				C[j][h][w]%=MODD;
				if (C[j][h][w]<0) C[j][h][w]+=MODD;
			}
		}
	}
	cout << ans*modpow(B(H*W,K),MODD-2)%MODD << endl;
}