#include <bits/stdc++.h>
using namespace std;

const int N = 1e6, Mod = 1e6 + 3;
#define LL long long

int n, k, a[N + 5], flag[N + 5], b[N + 5], tot;
LL fac[N + 5], ifac[N + 5];

void read(int &x) {
    x = 0; int w = 1; char c = getchar(); for(; c < '0' || c > '9'; c = getchar()) if (c == '-') w = -1;
    for(; c <= '9' && c >= '0'; c = getchar()) x = x * 10 + c - '0'; x *= w;
}

LL ksm(LL x, LL y) {
	LL res = 1;
	while(y) {
		if (y & 1)
			res = res * x % Mod;
		x = x * x % Mod;
		y >>= 1;
	} 
	return res;
}

void init(){
	fac[0] = 1;
	for(int i = 1; i <= N; ++i) fac[i] = fac[i - 1] * i % Mod;
	ifac[N] = ksm(fac[N], Mod - 2);
	for(int i = N - 1; i >= 0; --i)
		ifac[i] = ifac[i + 1] * (i + 1) % Mod;
}


LL C(int x, int y) {
	if (y > x) return 0;
	return fac[x] * ifac[y] % Mod * ifac[x - y] % Mod;
}

bool check(int x, int y) {
	if (x >= 0 && x <= 1 && y >= 0 && y <= 1) return 1;
	else return 0;
}

int main() {
	// freopen("sample5.in", "r", stdin);
	init();

	read(n); read(k);
	for(int i = 1; i <= n - k + 1; ++i)
		read(a[i]);

	for(int i = 1; i <= k; ++i) {
		int mi = 0, ma = 0, now = 0;
		for(int j = i; j + k <= n; j += k) {
			now += a[j + 1] - a[j];
			mi = min(mi, now);
			ma = max(ma, now);
		}
		if (!check(mi, ma) && !check(mi + 1, ma + 1)) {
			puts("-1");
			return 0;
		}
		if (check(mi, ma) && check(mi + 1, ma + 1)) continue;
		if (check(mi, ma)) b[i] = 0; else b[i] = 1;
		for(int j = i; j + k <= n; j += k)
		b[j + k] = b[j] + a[j + 1] - a[j];
		flag[i] = 1; ++tot;
		
	}
	tot = k - tot;
	for(int i = 1; i <= n; ++i) b[i] = b[i - 1] +  b[i];
	for(int i = 1; i + k - 1 <= n; ++i)
		a[i] -= b[i + k - 1] - b[i - 1];


	for(int i = 2; i <= n - k + 1; ++i)
		if (a[i] != a[1]) {
			puts("0");
			return 0;
		}	
	printf("%lld\n", C(tot, a[1]));
	return 0;
}
/*
b[i + 1] - b[i] = a[i + k] - a[i]


1 5  +1
2 6  +0
3 7  +0

*/