Mr. Chanek wants to knit a batik, a traditional cloth from Indonesia. The cloth forms a grid a with size n × m. There are k colors, and each cell in the grid can be one of the k colors.

Define a sub-rectangle as an ordered pair of two cells ((x_1, y_1), (x_2, y_2)), denoting the top-left cell and bottom-right cell (inclusively) of a sub-rectangle in a. Two sub-rectangles ((x_1, y_1), (x_2, y_2)) and ((x_3, y_3), (x_4, y_4)) have the same pattern if and only if the following holds: 

  * they have the same width (x_2 - x_1 = x_4 - x_3); 
  * they have the same height (y_2 - y_1 = y_4 - y_3); 
  * for every pair (i, j) where 0 ≤ i ≤ x_2 - x_1 and 0 ≤ j ≤ y_2 - y_1, the color of cells (x_1 + i, y_1 + j) and (x_3 + i, y_3 + j) are equal. 



Count the number of possible batik color combinations, such that the subrectangles ((a_x, a_y),(a_x + r - 1, a_y + c - 1)) and ((b_x, b_y),(b_x + r - 1, b_y + c - 1)) have the same pattern.

Output the answer modulo 10^9 + 7.

Input

The first line contains five integers n, m, k, r, and c (1 ≤ n, m ≤ 10^9, 1 ≤ k ≤ 10^9, 1 ≤ r ≤ min(10^6, n), 1 ≤ c ≤ min(10^6, m)) — the size of the batik, the number of colors, and size of the sub-rectangle.

The second line contains four integers a_x, a_y, b_x, and b_y (1 ≤ a_x, b_x ≤ n, 1 ≤ a_y, b_y ≤ m) — the top-left corners of the first and second sub-rectangle. Both of the sub-rectangles given are inside the grid (1 ≤ a_x + r - 1, b_x + r - 1 ≤ n, 1 ≤ a_y + c - 1, b_y + c - 1 ≤ m).

Output

Output an integer denoting the number of possible batik color combinations modulo 10^9 + 7.

Examples

Input


3 3 2 2 2
1 1 2 2


Output


32


Input


4 5 170845 2 2
1 4 3 1


Output


756680455

Note

The following are all 32 possible color combinations in the first example.

<image>
#include<bits/stdc++.h>
using namespace std;
 
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using ull = unsigned long long;
using vb = vector<bool>;
using vvb = vector<vb>;
using vd = vector<double>;
using vvd = vector<vd>;
using vvvd = vector<vvd>;
using vs = vector<string>;
using vvs = vector<vs>;
using vc = vector<char>;
using vvc = vector<vc>;
using ii = pair<int,int>;
using vii = vector<ii>;
using vvii = vector<vii>;
using dd = pair<double, double>;
using vdd = vector<dd>;
using vvdd = vector<vdd>;
using Mii = map<int,int>;
using vMii = vector<Mii>;
using Si = set<int>;
using vSi = vector<Si>;
using vvSi = vector<vSi>;
 
#define fi          first
#define se          second
#define INF         1e9 + 5
#define mod(a,m)    (a%m+m)%m
#define PB          push_back
#define MP          make_pair
#define all(a)      a.begin(), a.end()
 
const int mod = 1'000'000'007;

ll pow(ll base, ll exp) {
	if(exp == 0) return 1;
	ll temp = pow(base, exp>>1);
	if(exp&1) {
		return (((temp * temp) % mod) * base) % mod;
	}
	return (temp * temp) % mod;
}

 
int main(){
//	cout.setf(ios::fixed);
//	cout.precision(4);
	cin.tie(NULL);
	ios_base::sync_with_stdio(false);
	ll n, m, base, r, c;
	while(cin >> n >> m >> base >> r >> c) {
		int ax, bx, ay, by;
		cin >> ax >> bx >> ay >> by;
		ll ans = pow(base, n*m - r*c);
		cout << ans << '\n';
	}
}