Problem: Honestly, a rabbit does not matter.

There is a rabbit playing a stage system action game. In this game, every stage has a difficulty level. The rabbit, which always needs challenges, basically wants to play more difficult stages than he has ever played. However, he sometimes needs rest too. So, to compromise, he admitted to play T or less levels easier stages than the preceding one.

How many ways are there to play all the stages at once, while honoring the convention above? Maybe the answer will be a large number. So, let me know the answer modulo 1,000,000,007.



Input

The first line of input contains two integers N and T (1 ≤ N ≤ 100,000, 1 ≤ T ≤ 10,000). N is the number of stages, and T is the compromise level.

The following N lines describe the difficulty levels of each stage. The i-th line contains one integer Di (1 ≤ Di ≤ 100,000), which is the difficulty level of the i-th stage.

Output

Calculate how many ways to play all the stages at once there are. Print the answer modulo 1,000,000,007 in a line.

Examples

Input

3 1
1
2
3


Output

4


Input

5 3
9
2
6
8
8


Output

24


Input

5 7
9
9
9
1
5


Output

48

Solution (in CPP):

Solution:
#include <vector>
#include <iostream>
#include <utility>
#include <algorithm>
#include <string>
#include <deque>
#include <tuple>
#include <queue>
#include <functional>
#include <cmath>
#include <iomanip>
#include <map>
#include <numeric>
#include <unordered_map>
#include <unordered_set>
#include <complex>
#include <iterator>
#include <array>
#include <chrono>
//cin.sync_with_stdio(false);
//streambuf
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
using vi = vector<int>;
using vll = vector<ll>;
using vpii = vector<pii>;
template<class T, int s>using va = vector<array<T, s>>;
template<class T, class T2> using umap = unordered_map<T, T2>;
template<class T> using uset = unordered_set<T>;
template<class T, class S> void cmin(T &a, const S&&b) { if (a > b)a = b; }
template<class T, class S> void cmax(T &a, const S&&b) { if (a < b)a = b; }
#define ALL(a) a.begin(),a.end()
#define rep(i,a) for(int i=0;i<a;i++)
#define rep1(i,a) for(int i=1;i<=a;i++)
#define rrep(i,a) for(int i=a-1;i>=0;i--)
#define rrep1(i,a) for(int i=a;i;i--)
#ifndef INT_MAX
const int INT_MAX = numeric_limits<signed>().max();
#endif
template<class T>using heap = priority_queue<T, vector<T>, greater<T>>;
template<class T>using pque = priority_queue<T, vector<T>, function<T(T, T)>>;
template <class T>
inline void hash_combine(size_t & seed, const T & v) {
	hash<T> hasher;
	seed ^= hasher(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
}
namespace std {

	template<typename S, typename T> struct hash<pair<S, T>> {
		inline size_t operator()(const pair<S, T> & v) const {
			size_t seed = 0;
			hash_combine(seed, v.first);
			hash_combine(seed, v.second);
			return seed;
		}
	};
	// Recursive template code derived from Matthieu M.
	template <class Tuple, size_t Index = std::tuple_size<Tuple>::value - 1>
	struct HashValueImpl
	{
		static void apply(size_t& seed, Tuple const& tuple)
		{
			HashValueImpl<Tuple, Index - 1>::apply(seed, tuple);
			hash_combine(seed, std::get<Index>(tuple));
		}
	};

	template <class Tuple>
	struct HashValueImpl<Tuple, 0>
	{
		static void apply(size_t& seed, Tuple const& tuple)
		{
			hash_combine(seed, std::get<0>(tuple));
		}
	};

	template <typename ... TT>
	struct hash<std::tuple<TT...>>
	{
		size_t
			operator()(std::tuple<TT...> const& tt) const
		{
			size_t seed = 0;
			HashValueImpl<std::tuple<TT...> >::apply(seed, tt);
			return seed;
		}

	};
}
ll pow(ll base, ll i, ll mod) {
	ll a = 1;
	while (i) {
		if (i & 1) {
			a *= base;
			a %= mod;
		}
		base *= base;
		base %= mod;
		i /= 2;
	}
	return a;
}
class unionfind {
	vector<int> par, rank, size_;//????????§??????????????¢???????????????????????????rank???????????????size?????????
public:
	unionfind(int n) :par(n), rank(n), size_(n, 1) {
		iota(ALL(par), 0);
	}
	int find(int x) {
		if (par[x] == x)return x;
		return par[x] = find(par[x]);
	}
	void unite(int x, int y) {
		x = find(x), y = find(y);
		if (x == y)return;
		if (rank[x] < rank[y])swap(x, y);
		par[y] = x;
		size_[x] += size_[y];
		if (rank[x] == rank[y])rank[x]++;
	}
	bool same(int x, int y) {
		return find(x) == find(y);
	}
	int size(int x) {
		return size_[find(x)];
	}
};
ll gcd(ll a, ll b) {
	while (b) {
		ll c = a%b;
		a = b;
		b = c;
	}
	return a;
}
ll lcm(ll a, ll b) {
	return a / gcd(a, b)*b;
}
int popcnt(unsigned long long a) {
	a = (a & 0x5555555555555555) + (a >> 1 & 0x5555555555555555);
	a = (a & 0x3333333333333333) + (a >> 2 & 0x3333333333333333);
	a = (a & 0x0f0f0f0f0f0f0f0f) + (a >> 4 & 0x0f0f0f0f0f0f0f0f);
	a = (a & 0x00ff00ff00ff00ff) + (a >> 8 & 0x00ff00ff00ff00ff);
	a = (a & 0x0000ffff0000ffff) + (a >> 16 & 0x0000ffff0000ffff);
	return (a & 0xffffffff) + (a >> 32);
}
template<class T, class Func = function<T(T, T)>>
class segtree {
	vector<T> obj;
	int offset;
	Func updater;
	T e;
	int bufsize(int num) {
		int i = 1;
		for (; num >i; i <<= 1);
		offset = i - 1;
		return (i << 1) - 1;
	}
	T query(int a, int b, int k, int l, int r) {
		if (r <= a || b <= l)return e;
		if (a <= l && r <= b)return obj[k];
		else return updater(query(a, b, k * 2 + 1, l, (l + r) / 2), query(a, b, k * 2 + 2, (l + r) / 2, r));
	}
public:
	T query(int a, int b) {//[a,b)
		return query(a, b, 0, 0, offset + 1);
	}
	void updateall(int l = 0, int r = -1) {
		if (r < 0)r = offset + 1;
		l += offset, r += offset;
		do {
			l = l - 1 >> 1, r = r - 1 >> 1;
			for (int i = l; i < r; i++)obj[i] = updater(obj[i * 2 + 1], obj[i * 2 + 2]);
		} while (l);
	}
	void update(int k, T &a) {
		k += offset;
		obj[k] = a;
		while (k) {
			k = k - 1 >> 1;
			obj[k] = updater(obj[k * 2 + 1], obj[k * 2 + 2]);
		}
	}
	segtree(int n, T e, const Func &updater_ = Func()) :obj(bufsize(n), e), e(e), updater(updater_) {}
	segtree(vector<T> &vec, T e, const Func &updater = Func()) :obj(bufsize(vec.size()), e), e(e), updater(updater) {
		copy(vec.begin(), vec.end(), obj.begin() + offset);
		updateall();
	}
	typename vector<T>::reference operator[](int n) {
		return obj[n + offset];
	}
};
template<class T>
class matrix {
	vector<vector<T>> obj;
	pair<int, int> s;
public:
	matrix(pair<int, int> size, T e = 0) :matrix(size.first, size.second, e) {}
	matrix(int n, int m = -1, T e = 0) :obj(n, vector<T>(m == -1 ? n : m, e)), s(n, m == -1 ? n : m) {}
	static matrix e(int n) {
		matrix a = (n);
		for (int i = 0; i < n; i++)a[i][i] = 1;
		return a;
	}
	matrix& operator+=(const matrix &p) {
		if (s != p.s)throw runtime_error("matrix error");
		for (int i = 0; i < s.first; i++)
			for (int j = 0; j < s.second; j++)obj[i][j] += p.obj[i][j];
		return *this;
	}
	matrix operator+(const matrix &p) {
		matrix res(*this);
		return res += p;
	}
	matrix& operator-=(const matrix &p) {
		if (s != p.s)throw runtime_error("matrix error");
		for (int i = 0; i < s.first; i++)
			for (int j = 0; j < s.second; j++)obj[i][j] -= p.obj[i][j];
		return *this;
	}
	matrix operator-(const matrix &p) {
		matrix res(*this);
		return res -= p;
	}
	matrix& operator*=(T p) {
		for (auto &a : obj)
			for (auto &b : a)b *= p;
		return *this;
	}
	matrix operator*(T p) {
		matrix res(*this);
		return res *= p;
	}
	matrix operator*(const matrix &p) {
		if (s.second != p.s.first)throw runtime_error("matrix error");
		matrix ret(s.first, p.s.second);
		for (int i = 0; i < s.first; i++)
			for (int j = 0; j < s.second; j++)
				for (int k = 0; k < p.s.second; k++)ret[i][k] += obj[i][j] * p.obj[j][k];
		return ret;
	}
	matrix &operator*=(const matrix &p) {
		return *this = *this*p;
	}
	pair<int, int> size() const {
		return s;
	}
	matrix &mod(T m) {
		for (auto &a : obj)
			for (auto &b : a)b %= m;
		return *this;
	}
	typename vector<vector<T>>::reference operator[](int t) {
		return obj[t];
	}
};
template<class T> inline
matrix<T> pow(matrix<T> &base, unsigned exp) {
	auto base_(base);
	if (base_.size().first != base_.size().second)throw runtime_error("matrix error");
	matrix<T> res = matrix<T>::e(base_.size().first);
	for (;;) {
		if (exp & 1)res *= base_;
		if (!(exp /= 2))break;
		base_ *= base_;
	}
	return res;
}
template<class T> inline
matrix<T> modpow(matrix<T> &base, unsigned exp, T m) {
	auto base_(base);
	if (base.size().first != base_.size().second)throw runtime_error("matrix error");
	matrix<T> res = matrix<T>::e(base_.size().first);
	for (;;) {
		if (exp & 1)(res *= base_).mod(m);
		if (!(exp /= 2))break;
		(base_ *= base_).mod(m);
	}
	return res;
}
template<class T>int id(vector<T> &a, T b) {
	return lower_bound(ALL(a), b) - a.begin();
}
class Flow {
	int V;
	struct edge { int to, cap, rev, cost; };
	vector<vector<edge>> G;
	vector<int> level, iter, h, dist, prevv, preve;
	Flow(int size) :G(size + 1), V(size + 1) {
	}
	void add_edge(int from, int to, int cap, int cost = 0) {
		G[from].push_back(edge{ to, cap, (int)G[to].size(),cost });
		G[to].push_back(edge{ from,0,(int)G[from].size() - 1,-cost });
	}
	void bfs(int s) {
		fill(level.begin(), level.end(), -1);
		queue<int> que;
		level[s] = 0;
		que.push(s);
		while (!que.empty()) {
			int v = que.front(); que.pop();
			for (int i = 0; i < G[v].size(); i++) {
				edge &e = G[v][i];
				if (e.cap > 0 && level[e.to] < 0) {
					level[e.to] = level[v] + 1;
					que.push(e.to);
				}
			}
		}
	}
	int dfs(int v, int t, int f) {
		if (v == t)return f;
		for (int &i = iter[v]; i < G[v].size(); i++) {
			edge &e = G[v][i];
			if (e.cap > 0 && level[v] < level[e.to]) {
				int d = dfs(e.to, t, min(f, e.cap));
				if (d > 0) {
					e.cap -= d;
					G[e.to][e.rev].cap += d;
					return d;
				}
			}
		}
		return 0;
	}
	int max_flow(int s, int t) {
		level.resize(V);
		iter.resize(V);
		int flow = 0;
		for (;;) {
			bfs(s);
			if (level[t] < 0)return flow;
			fill(iter.begin(), iter.end(), 0);
			int f;
			while ((f = dfs(s, t, numeric_limits<int>::max()))>0) {
				flow += f;
			}
		}
	}
	typedef pair<int, int> P;
	int min_cost_flow(int s, int t, int f) {
		int res = 0;
		h.resize(V);
		dist.resize(V);
		prevv.resize(V);
		preve.resize(V);
		fill(h.begin(), h.end(), 0);
		while (f > 0) {
			priority_queue<P, vector<P>, greater<P>> que;
			fill(dist.begin(), dist.end(), numeric_limits<int>::max());
			dist[s] = 0;
			que.push({ 0,s });
			while (!que.empty()) {
				P p = que.top(); que.pop();
				int v = p.second;
				if (dist[v] < p.first)continue;
				for (int i = 0; i < G[v].size(); i++) {
					edge &e = G[v][i];
					if (e.cap > 0 && dist[e.to]>dist[v] + e.cost + h[v] - h[e.to]) {
						dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
						prevv[e.to] = v;
						preve[e.to] = i;
						que.push({ dist[e.to],e.to });
					}
				}
			}
			if (dist[t] == numeric_limits<int>::max()) {
				return -1;
			}
			for (int v = 0; v < V; v++)h[v] += dist[v];

			int d = f;
			for (int v = t; v != s; v = prevv[v]) {
				d = min(d, G[prevv[v]][preve[v]].cap);
			}
			f -= d;
			res += d*h[t];
			for (int v = t; v != s; v = prevv[v]) {
				edge &e = G[prevv[v]][preve[v]];
				e.cap -= d;
				G[v][e.rev].cap += d;
			}
		}
		return res;
	}
};
const ld eps = 1e-11, pi = acos(-1.0);
typedef complex<ld> P;
typedef vector<P> VP;
ld dot(P a, P b) { return real(conj(a) * b); }
ld cross(P a, P b) { return imag(conj(a) * b); }

namespace std {
	bool operator<(const P &a, const P &b) {
		return abs(a.real() - b.real()) < eps ? a.imag() < b.imag() : a.real() < b.real();
	}
}

struct L { P a, b; };//line->l,segment->s
struct C { P p; ld r; };

int ccw(P a, P b, P c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // counter clockwise
	if (cross(b, c) < -eps) return -1; // clockwise
	if (dot(b, c) < 0) return 2;       // c--a--b on line
	if (norm(b) < norm(c)) return -2;  // a--b--c on line
	return 0;                          // a--c--b on line
}

bool isis_ll(L l, L m) {//is intersect
	return abs(cross(l.b - l.a, m.b - m.a)) > eps;
}

bool isis_ls(L l, L s) {
	ld a = cross(l.b - l.a, s.a - l.a);
	ld b = cross(l.b - l.a, s.b - l.a);
	return (a * b < eps);
}

bool isis_lp(L l, P p) {
	return abs(cross(l.b - p, l.a - p)) < eps;
}

bool isis_ss(L s, L t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

P is_ll(L s, L t) { //intersect
	P sv = s.b - s.a, tv = t.b - t.a;
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

bool isis_sp(L s, P p) {
	return abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps;
}

P proj(L l, P p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

ld dist_lp(L l, P p) {
	return abs(p - proj(l, p));
}

ld dist_ll(L l, L m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

ld dist_ls(L l, L s) {
	if (isis_ls(l, s)) return 0;
	return min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(L s, P p) {
	P r = proj(s, p);
	if (isis_sp(s, r)) return abs(r - p);
	return min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(L s, L t) {
	if (isis_ss(s, t)) return 0;
	ld a = min(dist_sp(s, t.a), dist_sp(t, s.a));
	ld b = min(dist_sp(s, t.b), dist_sp(t, s.b));
	return min(a, b);
}

VP is_cc(C c1, C c2) {
	VP res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	P diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * P(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * P(rc, -rs));
	return res;
}

bool isis_vc(vector<C> vc) {
	VP crs;
	int n = vc.size();
	rep(i, n)rep(j, i)
		for (P p : is_cc(vc[i], vc[j]))
			crs.push_back(p);
	rep(i, n)
		crs.push_back(vc[i].p);
	for (P p : crs) {
		bool valid = true;
		rep(i, n)
			if (abs(p - vc[i].p)>vc[i].r + eps)
				valid = false;
		if (valid) return true;
	}
	return false;
}

VP is_lc(C c, L l) {
	VP res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		P nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

VP is_sc(C c, L l) {
	VP v = is_lc(c, l), res;
	for (P p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

vector<L> tangent_cp(C c, P p) {//????????\????
	vector<L> ret;
	P v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	P v1 = v * P(l / d, c.r / d);
	P v2 = v * P(l / d, -c.r / d);
	ret.push_back(L{ p, p + v1 });
	if (l < eps) return ret;
	ret.push_back(L{ p, p + v2 });
	return ret;
}

vector<L> tangent_cc(C c1, C c2) {
	vector<L> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		P center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		P out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<L> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		P v = c2.p - c1.p;
		v /= abs(v);
		P q1 = c1.p + v * P(0, 1) * c1.r;
		P q2 = c1.p + v * P(0, -1) * c1.r;
		ret.push_back(L{ q1, q1 + v });
		ret.push_back(L{ q2, q2 + v });
	}
	return ret;
}

ld area(const VP &p) {//??¢?????
	ld res = 0;
	int n = p.size();
	rep(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

bool is_polygon(L l, VP &g) {
	int n = g.size();
	for (int i = 0; i < n; i++) {
		P a = g[i];
		P b = g[(i + 1) % n];
		if (isis_ss(l, L{ a, b })) return true;
	}
	return false;
}

int is_in_Polygon(const VP &g, P p) {
	bool in = false;
	int n = g.size();
	for (int i = 0; i < n; i++) {
		P a = g[i] - p, b = g[(i + 1) % n] - p;
		if (imag(a) > imag(b)) swap(a, b);
		if (imag(a) <= 0 && 0 < imag(b))
			if (cross(a, b) < 0) in = !in;
		if (abs(cross(a, b)) < eps && dot(a, b) < eps) return 0; // on
	}
	if (in) return 1; // in
	return -1; // out
}

VP ConvexHull(VP ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	VP ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

VP ConvexCut(const VP &ps, L l) {
	VP Q;
	for (int i = 0; i < (int)ps.size(); i++) {
		P A = ps[i], B = ps[(i + 1) % ps.size()];
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0)
			Q.push_back(is_ll(L{ A, B }, l));
	}
	return Q;
}
double dist2(P a) {
	return real(a)*real(a) + imag(a)*imag(a);
}
// Suffix Array	?????????O(|S|log^2|S|), ????´¢O(|T|log|S|), ?????????????§????O(|S|)
class StringSearch {
	const int n;
	string S;
public:
	vector<int> sa, rank;
	StringSearch(const string &S_) :n(S_.size()), S(S_), sa(n + 1), rank(n + 1) {
		for (int i = 0; i <= n; i++) {
			sa[i] = i;
			rank[i] = i < n ? S[i] : -1;
		}
		vector<int> tmp(n + 1);
		for (int k = 1; k <= n; k *= 2) {
			auto Compare_SA = [=](int i, int j) {
				if (this->rank[i] != this->rank[j]) return this->rank[i] < this->rank[j];

				int ri = i + k <= n ? this->rank[i + k] : -1;
				int rj = j + k <= n ? this->rank[j + k] : -1;
				return ri < rj;
			};
			sort(sa.begin(), sa.end(), Compare_SA);
			tmp[sa[0]] = 0;
			for (int i = 1; i <= n; i++) {
				tmp[sa[i]] = tmp[sa[i - 1]] + (Compare_SA(sa[i - 1], sa[i]) ? 1 : 0);
			}
			for (int i = 0; i <= n; i++) {
				this->rank[i] = tmp[i];
			}
		}
	}
	bool Contain(const string &T) {
		int a = 0, b = n;
		while (b - a > 1) {
			int c = (a + b) / 2;
			if (S.compare(sa[c], T.length(), T) < 0) a = c;
			else b = c;
		}
		return S.compare(sa[b], T.length(), T) == 0;
	}
	vector<int> LCPArray() {
		for (int i = 0; i <= n; i++) rank[sa[i]] = i;
		int h = 0;
		vector<int> lcp(n + 1);
		for (int i = 0; i < n; i++) {
			int j = sa[rank[i] - 1];
			if (h > 0) h--;
			for (; j + h < n && i + h < n; h++) {
				if (S[j + h] != S[i + h]) break;
			}
			lcp[rank[i] - 1] = h;
		}
		return lcp;
	}
};
int main() {
	int n, t;
	cin >> n >> t;
	vi a(n);
	rep(i, n) {
		int l;
		cin >> l;
		a[i] = l;
	}
	sort(ALL(a));
	ll ans = 1;
	rep(i, n) {
		ans *= upper_bound(ALL(a), a[i] + t) - a.begin()-i;
		ans %= (int)1e9 + 7;
	}
	cout << ans << endl;
}