#include <bits/stdc++.h>
#define nl "\n"
#define no "NO"
#define yes "YES"
#define fi first
#define se second
#define vec vector
#define task "main"
#define _mp make_pair
#define ii pair<int, int>
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
#define evoid(val) return void(std::cout << val)
#define FOR(i, a, b) for(int i = (a); i <= (b); ++i)
#define FOD(i, b, a) for(int i = (b); i >= (a); --i)
#define unq(x) sort(all(x)); x.resize(unique(all(x)) - x.begin())
using namespace std;
template<typename U, typename V> bool maxi(U &a, V b) {
if (a < b) { a = b; return 1; } return 0;
}
template<typename U, typename V> bool mini(U &a, V b) {
if (a > b) { a = b; return 1; } return 0;
}
const int N = (int)1e6 + 9;
const int mod = (int)1e9 + 7;
void prepare(); void main_code();
int main() {
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
if (fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
const bool MULTITEST = 0; prepare();
int num_test = 1; if (MULTITEST) cin >> num_test;
while (num_test--) { main_code(); }
}
void prepare() {};
vector<int> g[N];
int a[N], id[N];
bool vis[N];
bool dfs(int u) {
vis[u] = 1;
for(int v : g[u]) {
if (id[v] == (id[u] ^ 1)) {
return 1;
}
if (!vis[v]) {
id[v] = id[u];
if (dfs(v)) return 1;
}
}
return 0;
}
int Pow(int a, long long b) {
int res = 1;
for(; b > 0; b >>= 1, a = 1ll * a * a % mod)
if (b & 1) res = 1ll * res * a % mod;
return res;
}
int add(int a, int b) { return a + b < mod ? a + b : a + b - mod; }
int sub(int a, int b) { return a >= b ? a - b : a - b + mod; }
int mul(int a, int b) { return 1LL * a * b % mod; }
void main_code() {
int n, k; cin >> n >> k;
for(int i = 1; i <= n; ++i) cin >> a[i + k - 1];
memset(id, -1, sizeof id);
for(int i = k + 1; i <= n; ++i) {
if (abs(a[i] - a[i - 1]) > 1) evoid(0);
if (a[i - 1] == a[i] - 1) {
if (id[i - k] == 1) evoid(0);
id[i - k] = 0, id[i] = 1;
} else if (a[i - 1] == a[i] + 1) {
if (id[i - k] == 0) evoid(0);
id[i - k] = 1, id[i] = 0;
} else {
g[i].push_back(i - k);
g[i - k].push_back(i);
}
}
for(int i = 1; i <= n; ++i) if (!vis[i] and id[i] != -1) {
if (dfs(i)) evoid(0);
}
// FOR(i, 1, n) cout << id[i] << ' ';
int sum = 0;
FOR(i, 1, k) {
if (id[i] != -1) sum += id[i];
}
int f = a[k] - sum;
if (f < 0) evoid(0);
FOR(i, k + 1, n) {
if (id[i-k]!=-1)
sum-=id[i-k];
if (id[i]!=-1)
sum+=id[i];
if (a[i]-sum != f)evoid(0);
}
// dem so bit
int t=0;
FOR(i, 1, k) if (id[i]==-1)++t;
// C(f, t)
// t! / f! * (t-f)!
vector<int> P(n+1,0);
P[0]=1;
FOR(i,1,n)P[i]=1LL*P[i-1]*i%mod;
if (t<f)evoid(0);
cout << mul(P[t], Pow(mul(P[f], P[t-f]) , mod-2));
}
/* Let the river flows naturally */
