#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>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
static const unsigned MODVAL = 1000000007;
struct mint
{
unsigned val;
mint() :val(0) {}
mint(int x) :val(x%MODVAL) {}
mint(unsigned x) :val(x%MODVAL) {}
mint(LL x) :val(x%MODVAL) {}
};
mint& operator+=(mint& x, mint y) { return x = x.val + y.val; }
mint& operator-=(mint& x, mint y) { return x = x.val - y.val + MODVAL; }
mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
mint operator+(mint x, mint y) { return x += y; }
mint operator-(mint x, mint y) { return x -= y; }
mint operator*(mint x, mint y) { return x *= y; }
class ShortBugPaths { public:
int count(int N, vector <int> D, int J)
{
if (N <= 200) {
vector<vector<int>> c(N, vector<int>(N, 1));
vector<vector<int>> c2(N, vector<int>(N, 1));
for (int _ = 0; _ < J; ++_) {
for (int y = 0; y < N; ++y)
for (int x = 0; x < N; ++x) {
LL sum = 0;
for (int DD : D) {
int yy = y - DD, xx = x;
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy<N && 0 <= xx&&xx<N) sum += c[yy][xx];
yy++, xx++;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy<N && 0 <= xx&&xx<N) sum += c[yy][xx];
yy++, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy<N && 0 <= xx&&xx<N) sum += c[yy][xx];
yy--, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy<N && 0 <= xx&&xx<N) sum += c[yy][xx];
yy--, xx++;
}
if (DD == 0)
sum += c[y][x];
}
c2[y][x] = sum % MODVAL;
}
c.swap(c2);
}
mint ans = 0;
for (int y = 0; y < N; ++y)
for (int x = 0; x < N; ++x)
ans += c[y][x];
return ans.val;
}
else {
vector<vector<int>> c(201, vector<int>(201, 1));
vector<vector<int>> c2(201, vector<int>(201, 1));
for (int _ = 0; _ < J; ++_) {
for (int y = 0; y < 101; ++y)
for (int x = 0; x < 101; ++x) {
LL sum = 0;
for (int DD : D) {
int yy = y - DD, xx = x;
if (y == 100 && x == 100) {
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[100][100];
yy++, xx++;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[100][100];
yy++, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[100][100];
yy--, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[100][100];
yy--, xx++;
}
}
else if (y == 100) {
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[100][min(100,xx)];
yy++, xx++;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[100][min(100, xx)];
yy++, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[100][min(100, xx)];
yy--, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[100][min(100, xx)];
yy--, xx++;
}
}
else if (x == 100) {
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[min(100, yy)][100];
yy++, xx++;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[min(100, yy)][100];
yy++, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[min(100, yy)][100];
yy--, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[min(100, yy)][100];
yy--, xx++;
}
}
else {
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[min(100, yy)][min(100, xx)];
yy++, xx++;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[min(100, yy)][min(100, xx)];
yy++, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[min(100, yy)][min(100, xx)];
yy--, xx--;
}
for (int d = 0; d < DD; ++d) {
if (0 <= yy&&yy < N && 0 <= xx&&xx < N) sum += c[min(100, yy)][min(100, xx)];
yy--, xx++;
}
}
if (DD == 0)
sum += c[y][x];
}
c2[y][x] = sum % MODVAL;
}
for (int y = 0; y < 201; ++y)
for (int x = 0; x < 201; ++x)
c2[y][x] = c2[y>100 ? 200-y : y][x>100 ? 200-x : x];
c.swap(c2);
}
mint ans = 0;
for (int y = 0; y < 201; ++y)
for (int x = 0; x < 201; ++x)
if (y == 100 && x == 100)
ans += mint(c[y][x]) * (N - 200) * (N - 200);
else if (y == 100 || x == 100)
ans += mint(c[y][x]) * (N - 200);
else
ans += c[y][x];
return ans.val;
}
}
};
// 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 int& Expected, const int& 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(_, ShortBugPaths().count(N, D, J));}
int main(){
CASE(0)
int N = 3;
int D_[] = {1};
vector <int> D(D_, D_+sizeof(D_)/sizeof(*D_));
int J = 1;
int _ = 24;
END
CASE(1)
int N = 123456789;
int D_[] = {0};
vector <int> D(D_, D_+sizeof(D_)/sizeof(*D_));
int J = 3;
int _ = 643499475;
END
CASE(2)
int N = 5;
int D_[] = {0, 10, 2};
vector <int> D(D_, D_+sizeof(D_)/sizeof(*D_));
int J = 4;
int _ = 38281;
END
CASE(3)
int N = 1000;
int D_[] = {0,1};
vector <int> D(D_, D_+sizeof(D_)/sizeof(*D_));
int J = 1;
int _ = 4996000;
END
CASE(4)
int N = 47;
int D_[] = {3};
vector <int> D(D_, D_+sizeof(D_)/sizeof(*D_));
int J = 6;
int _ = 195354165;
END
CASE(5)
int N = 200;
int D_[] = { 0,1,2,3,4,5,6,7,8,9,10 };
vector <int> D(D_, D_+sizeof(D_)/sizeof(*D_));
int J = 10;
int _ = 316860289;
END
CASE(6)
int N = 1000000000;
int D_[] = { 0,1,2,3,4,5,6,7,8,9,10 };
vector <int> D(D_, D_+sizeof(D_)/sizeof(*D_));
int J = 10;
int _ = -100;
END
}
// END CUT HERE