#include <iostream>
#include <algorithm>

typedef long long ll;
typedef double lf;

// #define DEBUG 1
struct IO
{
    #define MAXSIZE (1 << 20)
    #define isdigit(x) (x >= '0' && x <= '9')
    char buf[MAXSIZE], *p1, *p2;
    char pbuf[MAXSIZE], *pp;
    #if DEBUG
    #else
    IO() : p1(buf), p2(buf), pp(pbuf) {}
    ~IO() {fwrite(pbuf, 1, pp - pbuf, stdout);}
    #endif
    #define gc() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, MAXSIZE, stdin), p1 == p2) ? ' ' : *p1++)
    #define blank(x) (x == ' ' || x == '\n' || x == '\r' || x == '\t')

    template <typename T>
    void Read(T &x)
    {
        #if DEBUG
        std::cin >> x;
        #else
        bool sign = 0; char ch = gc(); x = 0;
        for (; !isdigit(ch); ch = gc())
            if (ch == '-') sign = 1;
        for (; isdigit(ch); ch = gc()) x = x * 10 + (ch ^ 48);
        if (sign) x = -x;
        #endif
    }
    void Read(char *s)
    {
        #if DEBUG
        std::cin >> s;
        #else
        char ch = gc();
        for (; blank(ch); ch = gc());
        for (; !blank(ch); ch = gc()) *s++ = ch;
        *s = 0;
        #endif
    }
    void Read(char &c) {for (c = gc(); blank(c); c = gc());}

    void Push(const char &c)
    {
        #if DEBUG
        putchar(c);
        #else
        if (pp - pbuf == MAXSIZE) fwrite(pbuf, 1, MAXSIZE, stdout), pp = pbuf;
        *pp++ = c;
        #endif
    }
    template <typename T>
    void Write(T x)
    {
        if (x < 0) x = -x, Push('-');
        static T sta[35];
        int top = 0;
        do sta[top++] = x % 10, x /= 10; while (x);
        while (top) Push(sta[--top] ^ 48);
    }
    template <typename T>
    void Write(T x, char lst) {Write(x), Push(lst);}
} IO;
#define Read(x) IO.Read(x)
#define Write(x, y) IO.Write(x, y)
#define Put(x) IO.Push(x)

using namespace std;

const int MAXN = 1e6 + 10, mod = 1e6 + 3;

int n, k, a[MAXN];

inline ll Qpow(ll x, int y)
{
    ll res = 1;
    while (y)
    {
        if (y & 1) res = res * x % mod;
        x = x * x % mod, y >>= 1;
    }
    return res;
}
inline ll C(int n, int m)
{
    ll res = 1, dv = 1;
    for (int i = n; i >= n - m + 1; i--) res = res * i % mod;
    for (int i = 2; i <= m; i++) dv = dv * i % mod;
    return res * Qpow(dv, mod - 2) % mod;
}

int fa[MAXN], col[MAXN];
int Find(int k) {return k == fa[k] ? k : fa[k] = Find(fa[k]);}
inline bool Union(int u, int v)
{
    u = Find(u), v = Find(v);
    if (u == v) return 1;
    if (~col[u] && ~col[v] && col[u] != col[v]) return 0;
    if (~col[u]) col[v] = col[u]; else col[u] = col[v];
    fa[u] = v;
    return 1;
}

int main()
{
    #if DEBUG
    #else
    ios::sync_with_stdio(0), cin.tie(0);
    #endif
    Read(n), Read(k);
    for (int i = 1; i <= n - k + 1; i++) Read(a[i]);
    for (int i = 1; i <= n; i++) fa[i] = i, col[i] = -1;
    bool flag = 1;
    for (int i = 1; i < n - k + 1; i++)
    {
        if (a[i] == a[i + 1] + 1)
        {
            if (col[Find(i)] == 0 || col[Find(i + k)] == 1) {flag = 0; break;}
            col[Find(i)] = 1, col[Find(i + k)] = 0;
        }
        else if (a[i] == a[i + 1] - 1)
        {
            if (col[Find(i)] == 1 || col[Find(i + k)] == 0) {flag = 0; break;}
            col[Find(i)] = 0, col[Find(i + k)] = 1;
        }
        else if (a[i] != a[i + 1]) {flag = 0; break;}
        else if (!Union(i, i + k)) {flag = 0; break;}
    }
    if (!flag) return Write(0, '\n'), 0;
    int sum = 0, cnt = 0;
    for (int i = 1; i <= k; i++)
        if (col[Find(i)] == 1) sum++;
        else if (col[Find(i)] == -1) cnt++;
    if (sum > a[1] || sum + cnt < a[1]) return Write(0, '\n'), 0;
    Write(C(cnt, a[1] - sum), '\n');
    return 0;
}