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#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); }