Periodni
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
using str = string; // yay python!
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
tcT > using PR = pair<T, T>;
// pairs
#define mp make_pair
#define f first
#define s second
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back
#define pf push_front
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define trav(a, x) for (auto &a : x)
const int MOD = 1e9 + 7; // 998244353;
const int MX = 2e5 + 5;
const ll INF = 1e18; // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until
// USACO updates ...
return x == 0 ? 0 : 31 - __builtin_clz(x);
} // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
ll cdiv(ll a, ll b) {
return a / b + ((a ^ b) > 0 && a % b);
} // divide a by b rounded up
ll fdiv(ll a, ll b) {
return a / b - ((a ^ b) < 0 && a % b);
} // divide a by b rounded down
tcT > bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
tcTU > T fstTrue(T lo, T hi, U f) {
hi++;
assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo) / 2;
f(mid) ? hi = mid : lo = mid + 1;
}
return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
lo--;
assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo + 1) / 2;
f(mid) ? lo = mid : hi = mid - 1;
}
return lo;
}
tcT > void remDup(vector<T> &v) { // sort and remove duplicates
sort(all(v));
v.erase(unique(all(v)), end(v));
}
tcTU > void erase(T &t, const U &u) { // don't erase
auto it = t.find(u);
assert(it != end(t));
t.erase(it);
} // element that doesn't exist from (multi)set
// INPUT
#define tcTUU tcT, class... U
tcT > void re(complex<T> &c);
tcTU > void re(pair<T, U> &p);
tcT > void re(V<T> &v);
tcT, size_t SZ > void re(AR<T, SZ> &a);
tcT > void re(T &x) { cin >> x; }
void re(db &d) {
str t;
re(t);
d = stod(t);
}
void re(ld &d) {
str t;
re(t);
d = stold(t);
}
tcTUU > void re(T &t, U &...u) {
re(t);
re(u...);
}
tcT > void re(complex<T> &c) {
T a, b;
re(a, b);
c = {a, b};
}
tcTU > void re(pair<T, U> &p) { re(p.f, p.s); }
tcT > void re(V<T> &x) { trav(a, x) re(a); }
tcT, size_t SZ > void re(AR<T, SZ> &x) { trav(a, x) re(a); }
tcT > void rv(int n, V<T> &x) {
x.rsz(n);
re(x);
}
// TO_STRING
#define ts to_string
str ts(char c) { return str(1, c); }
str ts(const char *s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
return b ? "true" : "false";
#else
return ts((int)b);
#endif
}
tcT > str ts(complex<T> c) {
stringstream ss;
ss << c;
return ss.str();
}
str ts(V<bool> v) {
str res = "{";
F0R(i, sz(v)) res += char('0' + v[i]);
res += "}";
return res;
}
template <size_t SZ> str ts(bitset<SZ> b) {
str res = "";
F0R(i, SZ) res += char('0' + b[i]);
return res;
}
tcTU > str ts(pair<T, U> p);
tcT > str ts(T v) { // containers with begin(), end()
#ifdef LOCAL
bool fst = 1;
str res = "{";
for (const auto &x : v) {
if (!fst) res += ", ";
fst = 0;
res += ts(x);
}
res += "}";
return res;
#else
bool fst = 1;
str res = "";
for (const auto &x : v) {
if (!fst) res += " ";
fst = 0;
res += ts(x);
}
return res;
#endif
}
tcTU > str ts(pair<T, U> p) {
#ifdef LOCAL
return "(" + ts(p.f) + ", " + ts(p.s) + ")";
#else
return ts(p.f) + " " + ts(p.s);
#endif
}
// OUTPUT
tcT > void pr(T x) { cout << ts(x); }
tcTUU > void pr(const T &t, const U &...u) {
pr(t);
pr(u...);
}
void ps() { pr("\n"); } // print w/ spaces
tcTUU > void ps(const T &t, const U &...u) {
pr(t);
if (sizeof...(u)) pr(" ");
ps(u...);
}
// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU > void DBG(const T &t, const U &...u) {
cerr << ts(t);
if (sizeof...(u)) cerr << ", ";
DBG(u...);
}
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
#define dbg(...) \
cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...) \
if (!(__VA_ARGS__)) \
cerr << "Line(" << __LINE__ << ") -> function(" << __FUNCTION__ \
<< ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", \
exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
void setPrec() { cout << fixed << setprecision(15); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
// FILE I/O
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
unsyncIO();
setPrec();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) setIn(s + ".in"), setOut(s + ".out"); // for USACO
}
/**
* Description: modular arithmetic operations
* Source:
* KACTL
* https://codeforces.com/blog/entry/63903
* https://codeforces.com/contest/1261/submission/65632855 (tourist)
* https://codeforces.com/contest/1264/submission/66344993 (ksun)
* also see https://github.com/ecnerwala/cp-book/blob/master/src/modnum.hpp
* (ecnerwal) Verification: https://open.kattis.com/problems/modulararithmetic
*/
template <int MOD, int RT> struct mint {
static const int mod = MOD;
static mint rt() { return RT; } // primitive root for FFT
int v;
explicit operator int() const { return v; } // don't silently convert to int
mint() { v = 0; }
mint(ll _v) {
v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
if (v < 0) v += MOD;
}
friend bool operator==(const mint &a, const mint &b) { return a.v == b.v; }
friend bool operator!=(const mint &a, const mint &b) { return !(a == b); }
friend bool operator<(const mint &a, const mint &b) { return a.v < b.v; }
friend void re(mint &a) {
ll x;
re(x);
a = mint(x);
}
friend str ts(mint a) { return ts(a.v); }
mint &operator+=(const mint &m) {
if ((v += m.v) >= MOD) v -= MOD;
return *this;
}
mint &operator-=(const mint &m) {
if ((v -= m.v) < 0) v += MOD;
return *this;
}
mint &operator*=(const mint &m) {
v = (ll)v * m.v % MOD;
return *this;
}
mint &operator/=(const mint &m) { return (*this) *= inv(m); }
friend mint pow(mint a, ll p) {
mint ans = 1;
assert(p >= 0);
for (; p; p /= 2, a *= a)
if (p & 1) ans *= a;
return ans;
}
friend mint inv(const mint &a) {
assert(a.v != 0);
return pow(a, MOD - 2);
}
mint operator-() const { return mint(-v); }
mint &operator++() { return *this += 1; }
mint &operator--() { return *this -= 1; }
friend mint operator+(mint a, const mint &b) { return a += b; }
friend mint operator-(mint a, const mint &b) { return a -= b; }
friend mint operator*(mint a, const mint &b) { return a *= b; }
friend mint operator/(mint a, const mint &b) { return a /= b; }
};
typedef mint<MOD, 3> mi;
typedef vector<mi> vmi;
typedef pair<mi, mi> pmi;
typedef vector<pmi> vpmi;
vector<vmi> scmb; // small combinations
void genComb(int SZ) {
scmb.assign(SZ, vmi(SZ));
scmb[0][0] = 1;
FOR(i, 1, SZ)
F0R(j, i + 1) scmb[i][j] = scmb[i - 1][j] + (j ? scmb[i - 1][j - 1] : 0);
}
/**
* Description: pre-compute factorial mod inverses,
* assumes $MOD$ is prime and $SZ < MOD$.
* Time: O(SZ)
* Source: KACTL
* Verification: https://dmoj.ca/problem/tle17c4p5
*/
vi invs, fac,
ifac; // make sure to convert to LL before doing any multiplications ...
void genFac(int SZ) {
invs.rsz(SZ), fac.rsz(SZ), ifac.rsz(SZ);
invs[1] = fac[0] = ifac[0] = 1;
FOR(i, 2, SZ) invs[i] = MOD - (ll)MOD / i * invs[MOD % i] % MOD;
FOR(i, 1, SZ) {
fac[i] = (ll)fac[i - 1] * i % MOD;
ifac[i] = (ll)ifac[i - 1] * invs[i] % MOD;
}
}
ll comb(int a, int b) {
if (a < b || b < 0) return 0;
return (ll)fac[a] * ifac[b] % MOD * ifac[a - b] % MOD;
}
int N, K;
vi h;
vmi comb(vmi a, vmi b) {
vmi c(sz(a) + sz(b) - 1);
F0R(i, sz(a)) F0R(j, sz(b)) c[i + j] += a[i] * b[j];
return c;
}
vmi tran(vmi a, int b) {
R0F(i, sz(a))
FOR(j, i + 1, sz(a))
a[j] += mi(fac[j - i]) * comb(sz(a) - 1 - i, j - i) * comb(b, j - i) * a[i];
return a;
}
vmi solve(int l, int r, int cur) {
if (l > r) return {1};
int mn = l;
FOR(i, l, r + 1) if (h[i] < h[mn]) mn = i;
vmi a = solve(l, mn - 1, h[mn]), b = solve(mn + 1, r, h[mn]);
vmi c = comb(a, b);
c.pb(0);
c = tran(c, h[mn] - cur);
return c;
}
int main() {
genFac(1000005);
setIO();
re(N, K);
h.rsz(N);
re(h);
vmi v = solve(0, N - 1, 0);
ps(K < sz(v) ? v[K] : 0);
}