/*
 _____ _             _              _           _
|_   _| |__   ___   / \   _ __  ___| |__  _   _| |
  | | | '_ \ / _ \ / _ \ | '_ \/ __| '_ \| | | | |
  | | | | | |  __// ___ \| | | \__ \ | | | |_| | |
  |_| |_| |_|\___/_/   \_\_| |_|___/_| |_|\__,_|_|

*/
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll          long long
#define pb          push_back
#define ppb         pop_back
#define	endl		'\n'
#define mii         map<ll,ll>
#define msi         map<string,ll>
#define mis         map<ll, string>
#define rep(i,a,b)    for(ll i=a;i<b;i++)
#define repr(i,a,b) for(ll i=b-1;i>=a;i--)
#define trav(a, x) 	for(auto& a : x)
#define pii         pair<ll,ll>
#define vi          vector<ll>
#define vii         vector<pair<ll, ll>>
#define vs          vector<string>
#define all(a)      (a).begin(),(a).end()
#define F           first
#define S           second
#define sz(x)       (ll)x.size()
#define hell        1000000007
#define lbnd        lower_bound
#define ubnd        upper_bound
#define max(a,b)	(a>b?a:b)
#define min(a,b)	(a<b?a:b)

/*	For Debugging	*/
#define DEBUG 		cerr<<"\n>>>I'm Here<<<\n"<<endl;
#define display(x) trav(a,x) cout<<a<<" ";cout<<endl;
#define what_iss(x)  cerr << #x << " = " << x << endl;
#define what_is(x)  cerr << #x << " = " << x << " ";

std::mt19937_64 rng(std::chrono::steady_clock::now().time_since_epoch().count());
#define ordered_set tree<ll, null_type,less<ll>, rb_tree_tag,tree_order_statistics_node_update>
#define TIME        cerr << "\nTime elapsed: " << setprecision(5) <<1000.0 * clock() / CLOCKS_PER_SEC << "ms\n";
#define DECIMAL(n)  cout << fixed ; cout << setprecision(n);
#define FAST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace __gnu_pbds;
using namespace std;
#define PI 3.141592653589793
#define N  1005
ll dp[N][N];
ll n,m,r;
ll fact[N],modi[N];

ll add(ll a,ll b,ll mod=hell)
{
	return (a+b)%mod;
}
ll sub(ll a,ll b,ll mod=hell)
{
	return (a-b+mod)%mod;
}
ll mul(ll a,ll b,ll mod=hell)
{
	return (a*b)%mod;
}

ll nCr(ll n,ll r) {
	return mul(fact[n], mul(modi[r], modi[n-r]));
}

ll expo(ll base, ll exponent, ll mod) {								//return base^exponent modulo modulus
    ll ans = 1;
    while(exponent !=0 ) {
        if((exponent&1) == 1) {
            ans = ans*base ;
            ans = ans%mod;
        }
        base = base*base;
        base %= mod;
        exponent>>= 1;
    }
    return ans%mod;
}

ll fun(pii p1,pii p2) {
	if((p1.F - r > p2.F + r) || (p1.F + r < p2.F - r) || (p1.S - r > p2.S + r) || (p1.S + r < p2.S - r))
		return 0;
	// what_is(p1.F);
	// what_is(p1.S);
	// what_is(p2.F);
	// what_is(p2.S);
	ll x1 = min(max(p1.F+r,p2.F-r), max(p1.F-r,p2.F+r));
	ll x2 = max(min(p1.F+r,p2.F-r), min(p1.F-r,p2.F+r));
	ll y1 = min(max(p1.S+r,p2.S-r), max(p1.S-r,p2.S+r));
	ll y2 = max(min(p1.S+r,p2.S-r), min(p1.S-r,p2.S+r));
	// what_is(x1);
	// what_is(x2);
	// what_is(y1);
	// what_iss(y2);
	x2 = max(x2 - 1, 0);
	y2 = max(y2 - 1, 0);
	return (dp[x1][y1] + dp[x2][y1] - dp[x1][y2] - dp[x2][y1]);
}


void solve()
{
	cin >> n >> m >> r;
	vector<pair<pii,ll>> v(n);

	ll nCm = nCr(n,m);

	rep(i,0,n) {
		cin >> v[i].F.F >> v[i].F.S >> v[i].S;
		v[i].F.F++;
		v[i].F.S++;
		dp[v[i].F.F][v[i].F.S] = 1;
	}
	rep(i,0,N) {
		rep(j,1,N) {
			dp[i][j] += dp[i][j-1];
		}
	}
	rep(j,0,N) {
		rep(i,1,N) {
			dp[i][j] += dp[i-1][j];
		}
	}
	ll ans = 0;
	ll k;
	rep(i, 0, n) {
		rep(j, i, n) {
			k  = fun(v[i].F,v[j].F);
			// what_is(i);
			// what_is(j);
			// what_iss(k);
			ans = add(ans, mul(sub(nCm, nCr(n - k, m)), mul(v[i].S, v[j].S)));
		}
	}
	cout << ans << endl;
	return;
}
int main()
{
	fact[0] = 1;
	rep(i,1,2*N) {
		fact[i] = (fact[i-1] * i) % hell;
	}
	rep(i,2,n+1) {
		modi[i] = expo(fact[i], hell - 2, hell);
	}
	FAST
	int TESTS=1;
//	cin>>TESTS;
	rep(i,0,TESTS)
    {
        // cout<<"Case #"<<i+1<<": ";
        solve();
    }
	// TIME
	return 0;
}