Problem: There are N children, numbered 1,2,\ldots,N. In the next K days, we will give them some cookies. In the i-th day, we will choose a_i children among the N with equal probability, and give one cookie to each child chosen. (We make these K choices independently.)

Let us define the happiness of the children as c_1 \times c_2 \times \ldots \times c_N, where c_i is the number of cookies received by Child i in the K days. Find the expected happiness multiplied by \binom{N}{a_1} \times \binom{N}{a_2} \times \ldots \times \binom{N}{a_K} (we can show that this value is an integer), modulo (10^{9}+7).

Constraints

* 1 \leq N \leq 1000
* 1 \leq K \leq 20
* 1 \leq a_i \leq N

Input

Input is given from Standard Input in the following format:


N K
a_1 a_2 \ldots a_K


Output

Print the answer.

Examples

Input

3 2
3 2


Output

12


Input

856 16
399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63


Output

337587117

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

#define debug(...) fprintf(stderr, __VA_ARGS__)

#ifndef AT_HOME
#define getchar() IO::myGetchar()
#define putchar(x) IO::myPutchar(x)
#endif

namespace IO {
	static const int IN_BUF = 1 << 23, OUT_BUF = 1 << 23;

	inline char myGetchar() {
		static char buf[IN_BUF], *ps = buf, *pt = buf;
		if (ps == pt) {
			ps = buf, pt = buf + fread(buf, 1, IN_BUF, stdin);
		}
		return ps == pt ? EOF : *ps++;
	}

	template<typename T>
	inline bool read(T &x) {
		bool op = 0;
		char ch = getchar();
		x = 0;
		for (; !isdigit(ch) && ch != EOF; ch = getchar()) {
			op ^= (ch == '-');
		}
		if (ch == EOF) {
			return false;
		}
		for (; isdigit(ch); ch = getchar()) {
			x = x * 10 + (ch ^ '0');
		}
		if (op) {
			x = -x;
		}
		return true;
	}

	inline int readStr(char *s) {
		int n = 0;
		char ch = getchar();
		for (; isspace(ch) && ch != EOF; ch = getchar())
			;
		for (; !isspace(ch) && ch != EOF; ch = getchar()) {
			s[n++] = ch;
		}
		s[n] = '\0';
		return n;
	}

	inline void myPutchar(char x) {
		static char pbuf[OUT_BUF], *pp = pbuf;
		struct _flusher {
			~_flusher() {
				fwrite(pbuf, 1, pp - pbuf, stdout);
			}
		};
		static _flusher outputFlusher;
		if (pp == pbuf + OUT_BUF) {
			fwrite(pbuf, 1, OUT_BUF, stdout);
			pp = pbuf;
		}
		*pp++ = x;
	}

	template<typename T>
	inline void print_(T x) {
		if (x == 0) {
			putchar('0');
			return;
		}
		static int num[40];
		if (x < 0) {
			putchar('-');
			x = -x;
		}
		for (*num = 0; x; x /= 10) {
			num[++*num] = x % 10;
		}
		while (*num){
			putchar(num[*num] ^ '0');
			--*num;
		}
	}

	template<typename T>
	inline void print(T x, char ch = '\n') {
		print_(x);
		putchar(ch);
	}

	inline void printStr_(const char *s, int n = -1) {
		if (n == -1) {
			n = strlen(s);
		}
		for (int i = 0; i < n; ++i) {
			putchar(s[i]);
		}
	}

	inline void printStr(const char *s, int n = -1, char ch = '\n') {
		printStr_(s, n);
		putchar(ch);
	}
}
using namespace IO;

const int N = 1005, P = 1000000007;

int n, m, a[N], inv[N], C[N][N], f[N];

int main() {
	read(n), read(m);
	for (int i = 1; i <= m; ++i) {
		read(a[i]);
	}
	inv[1] = 1;
	for (int i = 2; i <= n; ++i) {
		inv[i] = 1ll * (P - P / i) * inv[P % i] % P;
	}
	inv[0] = 1;
	for (int i = 1; i <= n; ++i) {
		inv[i] = 1ll * inv[i] * inv[i - 1] % P;
	}
	for (int i = 0; i <= n; ++i) {
		C[i][0] = C[i][i] = 1;
		for (int j = 1; j < i; ++j) {
			C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % P;
		}
	}
	f[0] = 1;
	for (int i = 1; i <= m; ++i) {
		for (int j = n; j >= 0; --j) {
			int sum = 0;
			for (int k = 0; k <= a[i] && k <= j; ++k) {
				sum = (sum + 1ll * f[j - k] * C[n - k][a[i] - k] % P * inv[k]) % P;
			}
			f[j] = sum;
		}
	}
	int ans = f[n];
	for (int i = 1; i <= n; ++i) {
		ans = 1ll * ans * i % P;
	}
	print(ans);
}