#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<double> CMP;
template<typename T>
vector<int> compress(const vector<T>& xs, int origin = 0)
{
vector< pair<T,int> > xi;
for(int i=0; i<xs.size(); ++i)
xi.push_back( make_pair(xs[i], i) );
sort(xi.begin(), xi.end());
vector<int> result(xs.size());
for(int k=0,id=origin; k<xi.size(); ++k) {
if(0<=k-1 && xi[k-1].first<xi[k].first)
++id;
result[xi[k].second] = id;
}
return result;
}
std::vector<int> compress(const std::vector<int>& xs) // convert to 1-origin rank
{
set<int> s(xs.begin(), xs.end());
map<int,int> mp;
int ID = 1;
for(set<int>::iterator it=s.begin(); it!=s.end(); ++it)
mp[*it] = ID++;
std::vector<int> result(xs.size());
for(int k=0; k<xs.size(); ++k)
result[k] = mp[xs[k]];
return result;
}
LL C(LL n, LL k)
{
if(n<k)
return 0;
k = min(k, n-k);
LL c = 1;
for(LL i=0; i<k; ++i)
c *= n-i, c /= i+1;
return c;
}
class Excavations { public:
long long count(vector <int> kind, vector <int> depth, vector <int> found, int K)
{
depth = compress(depth, 1);
int MD = *max_element(depth.begin(), depth.end());
map< int, vector<int> > kind_to_depth;
set<int> found_set(found.begin(), found.end());
for(int i=0; i<kind.size(); ++i)
kind_to_depth[kind[i]].push_back(depth[i]);
vector< vector<LL> > tbl_f(K+1, vector<LL>(MD+1));
vector< vector<LL> > tbl_nf(K+1, vector<LL>(MD+1));
for(int d=0; d<=MD; ++d)
tbl_f[0][d] = tbl_nf[0][d] = 1;
for(map<int,vector<int> >::iterator it=kind_to_depth.begin(); it != kind_to_depth.end(); ++it) {
bool f = !!found_set.count(it->first);
vector<int> ds = it->second;
sort(ds.begin(), ds.end());
vector< vector<LL> > tbl2 = calc_table(K, MD, ds, f);
vector< vector<LL> >& tbl = (f ? tbl_f : tbl_nf);
tbl = combine(K, MD, tbl, tbl2);
}
LL total = 0;
for(int k=0; k<=K; ++k)
total += cross(tbl_f[k], tbl_nf[K-k]);
return total;
}
LL cross(const vector<LL>& f, const vector<LL>& n)
{
vector< pair<int,LL> > pf;
for(int d=0; d<f.size(); ++d) {
LL cnt = (d==0 ? f[d] : f[d]-f[d-1]);
if(cnt) {
pf.push_back(make_pair(d, cnt));
}
}
vector< pair<int,LL> > nf;
for(int d=0; d<n.size(); ++d) {
LL cnt = (d==n.size()-1 ? n[d] : n[d]-n[d+1]);
if(cnt) {
nf.push_back(make_pair(d, cnt));
}
}
LL total = 0;
for(int i=0; i<pf.size(); ++i)
for(int k=0; k<nf.size(); ++k)
{
if(pf[i].first <= nf[k].first)
total += pf[i].second * nf[k].second;
}
return total;
}
vector< vector<LL> > calc_table(int K, int D, const vector<int>& ds, bool found)
{
vector< vector<LL> > tbl(K+1, vector<LL>(D+1));
for(int d=0; d<=D; ++d)
{
int num_discover = upper_bound(ds.begin(), ds.end(), d) - ds.begin();
for(int k=0; k<=K; ++k)
tbl[k][d] = (found ? (k==0 ? 0 : C(num_discover, k)) : C(ds.size()-num_discover, k));
}
return tbl;
}
vector< vector<LL> > combine(int K, int D, const vector<vector<LL> >& s, const vector<vector<LL> >& t)
{
vector< vector<LL> > r(K+1, vector<LL>(D+1));
for(int ks=0; ks<=K; ++ks)
for(int kt=0; kt<=K; ++kt) if(ks+kt<=K)
for(int d=0; d<=D; ++d)
r[ks+kt][d] += s[ks][d] * t[kt][d];
return r;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const long long& Expected, const long long& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, Excavations().count(kind, depth, found, K));}
int main(){
CASE(0)
int kind_[] = {1, 1, 2, 2};
vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
int depth_[] = {10, 15, 10, 20};
vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
int found_[] = {1};
vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
int K = 2;
long long _ = 3LL;
END
CASE(1)
int kind_[] = {1, 1, 2, 2};
vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
int depth_[] = {10, 15, 10, 20};
vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
int found_[] = {1, 2};
vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
int K = 2;
long long _ = 4LL;
END
CASE(2)
int kind_[] = {1, 2, 3, 4};
vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
int depth_[] = {10, 10, 10, 10};
vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
int found_[] = {1, 2};
vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
int K = 3;
long long _ = 0LL;
END
CASE(3)
int kind_[] = {1, 2, 2, 3, 1, 3, 2, 1, 2};
vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
int depth_[] = {12512, 12859, 125, 1000, 99, 114, 125, 125, 114};
vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
int found_[] = {1, 2, 3};
vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
int K = 7;
long long _ = 35LL;
END
CASE(4)
int kind_[] = {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50};
vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
int depth_[] = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3};
vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
int found_[] = {50};
vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
int K = 18;
long long _ = 9075135300LL;
END
/*
CASE(5)
int kind_[] = ;
vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
int depth_[] = ;
vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
int found_[] = ;
vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
int K = ;
long long _ = LL;
END
CASE(6)
int kind_[] = ;
vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
int depth_[] = ;
vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
int found_[] = ;
vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
int K = ;
long long _ = LL;
END
*/
}
// END CUT HERE