#include <bits/stdc++.h>
const double pi = 3.141592653589793238462643383279;
namespace MyMinMax {
template <typename T>
inline T mn(const T x, const T y) {
  return x < y ? x : y;
}
template <typename T>
inline T mx(const T x, const T y) {
  return x > y ? x : y;
}
template <typename T>
inline bool chmin(T &x, const T y) {
  return (x > y) && ((x = y), 1);
}
template <typename T>
inline bool chmax(T &x, const T y) {
  return (x < y) && ((x = y), 1);
}
template <typename T, typename... Args>
inline T mx(const T x, const Args... args) {
  return mx(x, mx(args...));
}
template <typename T, typename... Args>
inline T mn(const T x, const Args... args) {
  return mn(x, mn(args...));
}
}  // namespace MyMinMax
using namespace MyMinMax;
namespace IO {
const int DPAIRSIZ = 1 << 18;
char BB[DPAIRSIZ], *SS = BB, *TT = BB;
inline char getcha() {
  return SS == TT && (TT = (SS = BB) + fread(BB, 1, DPAIRSIZ, stdin), SS == TT)
             ? EOF
             : *SS++;
}
template <typename T = int>
inline T read() {
  T x = 0;
  int fu = 1;
  char c = getcha();
  while (c > 57 || c < 48) {
    if (c == 45) fu = -1;
    c = getcha();
  }
  while (c <= 57 && c >= 48) {
    x = x * 10 + c - 48;
    c = getcha();
  }
  x *= fu;
  return x;
}
template <typename T>
inline void read(T &x) {
  x = 0;
  int fu = 1;
  char c = getcha();
  while (c > 57 || c < 48) {
    if (c == 45) fu = -1;
    c = getcha();
  }
  while (c <= 57 && c >= 48) {
    x = x * 10 + c - 48;
    c = getcha();
  }
  x *= fu;
}
template <typename T>
inline void read(T *bg, T *ed) {
  while (bg != ed) read(*bg++);
}
inline void read(char &ch) {
  ch = getcha();
  while (ch <= 32) ch = getcha();
}
inline void read(char *s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void sread(char *s) {
  char ch = getcha();
  while (ch < 32) ch = getcha();
  while (ch >= 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void pread(char *&s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void spread(char *&s) {
  char ch = getcha();
  while (ch < 32) ch = getcha();
  while (ch >= 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
template <typename T, typename... Args>
inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}
char out[DPAIRSIZ], *Out = out;
inline void putcha(char x) {
  *Out++ = x;
  if (Out - out >= (DPAIRSIZ)) fwrite(out, 1, Out - out, stdout), Out = out;
}
template <typename T>
inline void fprint(T x) {
  if (x < 0) putcha(45), x = -x;
  if (x > 9) fprint(x / 10);
  putcha(x % 10 + 48);
}
inline void print() { putcha(10); }
template <typename T>
inline void print(T x) {
  fprint(x);
  putcha(10);
}
inline void print(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
inline void print(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
template <typename T, typename... Args>
inline void print(T x, Args... args) {
  fprint(x);
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename T, typename... Args>
inline void printl(T x, Args... args) {
  fprint(x);
  putcha(10);
  printl(args...);
}
template <typename... Args>
inline void printl(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  printl(args...);
}
template <typename... Args>
inline void printl(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  printl(args...);
}
template <typename T>
inline void sprint(T x) {
  fprint(x);
  putcha(32);
}
template <typename T, typename... Args>
inline void sprint(T x, Args... args) {
  fprint(x);
  putcha(32);
  sprint(args...);
}
template <typename T>
inline void sprint(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
}
template <typename T>
inline void print(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
  putcha(10);
}
template <typename T>
inline void printl(T *bg, T *ed) {
  while (bg != ed) print(*bg++);
}
class AutoFlush {
 public:
  ~AutoFlush() { fwrite(out, 1, Out - out, stdout); }
} __AutoFlush;
}  // namespace IO
using namespace IO;
const int INF = 0x3f3f3f3f;
const long long INFll = 0x3f3f3f3f3f3f3f3fll;
const int MAXN = 5005, MOD = 1e9 + 7;
int n, k, f[MAXN];
inline int ksm(int x, int y) {
  int ret = 1;
  while (y) {
    if (y & 1) ret = 1ll * ret * x % MOD;
    x = 1ll * x * x % MOD;
    y >>= 1;
  }
  return ret;
}
inline void Add(int &x, const int y) { ((x += y) >= MOD) && (x -= MOD); }
signed main() {
  read(n, k);
  f[0] = 1;
  for (int i = (1); i <= (n); ++i) {
    const int x = read();
    for (int j = (i); j >= (1); --j)
      f[j] = (1ll * f[j] * x - f[j - 1] + MOD) % MOD;
    f[0] = 1ll * f[0] * x % MOD;
  }
  const int inv = ksm(n, MOD - 2);
  int ans = 0, cur = 1;
  for (int j = (0); j <= (n); ++j) {
    Add(ans, 1ll * f[j] * cur % MOD);
    cur = 1ll * cur * inv % MOD * (k - j) % MOD;
  }
  print((f[0] - ans + MOD) % MOD);
}

### Prompt

Your task is to create a cpp solution to the following problem:

A false witness that speaketh lies!

You are given a sequence containing n integers. There is a variable res that is equal to 0 initially. The following process repeats k times.

Choose an index from 1 to n uniformly at random. Name it x. Add to res the multiply of all ai's such that 1 ≤ i ≤ n, but i ≠ x. Then, subtract ax by 1.

You have to find expected value of res at the end of the process. It can be proved that the expected value of res can be represented as an irreducible fraction <image>. You have to find <image>.

Input

The first line contains two integers n and k (1 ≤ n ≤ 5000, 1 ≤ k ≤ 109) — the number of elements and parameter k that is specified in the statement.

The second line contains n space separated integers a1, a2, ..., an (0 ≤ ai ≤ 109).

Output

Output a single integer — the value <image>.

Examples

Input

2 1
5 5


Output

5

Input

1 10
80


Output

10

Input

2 2
0 0


Output

500000003

Input

9 4
0 11 12 9 20 7 8 18 2


Output

169316356

### Response

```cpp
#include <bits/stdc++.h>
const double pi = 3.141592653589793238462643383279;
namespace MyMinMax {
template <typename T>
inline T mn(const T x, const T y) {
  return x < y ? x : y;
}
template <typename T>
inline T mx(const T x, const T y) {
  return x > y ? x : y;
}
template <typename T>
inline bool chmin(T &x, const T y) {
  return (x > y) && ((x = y), 1);
}
template <typename T>
inline bool chmax(T &x, const T y) {
  return (x < y) && ((x = y), 1);
}
template <typename T, typename... Args>
inline T mx(const T x, const Args... args) {
  return mx(x, mx(args...));
}
template <typename T, typename... Args>
inline T mn(const T x, const Args... args) {
  return mn(x, mn(args...));
}
}  // namespace MyMinMax
using namespace MyMinMax;
namespace IO {
const int DPAIRSIZ = 1 << 18;
char BB[DPAIRSIZ], *SS = BB, *TT = BB;
inline char getcha() {
  return SS == TT && (TT = (SS = BB) + fread(BB, 1, DPAIRSIZ, stdin), SS == TT)
             ? EOF
             : *SS++;
}
template <typename T = int>
inline T read() {
  T x = 0;
  int fu = 1;
  char c = getcha();
  while (c > 57 || c < 48) {
    if (c == 45) fu = -1;
    c = getcha();
  }
  while (c <= 57 && c >= 48) {
    x = x * 10 + c - 48;
    c = getcha();
  }
  x *= fu;
  return x;
}
template <typename T>
inline void read(T &x) {
  x = 0;
  int fu = 1;
  char c = getcha();
  while (c > 57 || c < 48) {
    if (c == 45) fu = -1;
    c = getcha();
  }
  while (c <= 57 && c >= 48) {
    x = x * 10 + c - 48;
    c = getcha();
  }
  x *= fu;
}
template <typename T>
inline void read(T *bg, T *ed) {
  while (bg != ed) read(*bg++);
}
inline void read(char &ch) {
  ch = getcha();
  while (ch <= 32) ch = getcha();
}
inline void read(char *s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void sread(char *s) {
  char ch = getcha();
  while (ch < 32) ch = getcha();
  while (ch >= 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void pread(char *&s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void spread(char *&s) {
  char ch = getcha();
  while (ch < 32) ch = getcha();
  while (ch >= 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
template <typename T, typename... Args>
inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}
char out[DPAIRSIZ], *Out = out;
inline void putcha(char x) {
  *Out++ = x;
  if (Out - out >= (DPAIRSIZ)) fwrite(out, 1, Out - out, stdout), Out = out;
}
template <typename T>
inline void fprint(T x) {
  if (x < 0) putcha(45), x = -x;
  if (x > 9) fprint(x / 10);
  putcha(x % 10 + 48);
}
inline void print() { putcha(10); }
template <typename T>
inline void print(T x) {
  fprint(x);
  putcha(10);
}
inline void print(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
inline void print(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
template <typename T, typename... Args>
inline void print(T x, Args... args) {
  fprint(x);
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename T, typename... Args>
inline void printl(T x, Args... args) {
  fprint(x);
  putcha(10);
  printl(args...);
}
template <typename... Args>
inline void printl(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  printl(args...);
}
template <typename... Args>
inline void printl(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  printl(args...);
}
template <typename T>
inline void sprint(T x) {
  fprint(x);
  putcha(32);
}
template <typename T, typename... Args>
inline void sprint(T x, Args... args) {
  fprint(x);
  putcha(32);
  sprint(args...);
}
template <typename T>
inline void sprint(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
}
template <typename T>
inline void print(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
  putcha(10);
}
template <typename T>
inline void printl(T *bg, T *ed) {
  while (bg != ed) print(*bg++);
}
class AutoFlush {
 public:
  ~AutoFlush() { fwrite(out, 1, Out - out, stdout); }
} __AutoFlush;
}  // namespace IO
using namespace IO;
const int INF = 0x3f3f3f3f;
const long long INFll = 0x3f3f3f3f3f3f3f3fll;
const int MAXN = 5005, MOD = 1e9 + 7;
int n, k, f[MAXN];
inline int ksm(int x, int y) {
  int ret = 1;
  while (y) {
    if (y & 1) ret = 1ll * ret * x % MOD;
    x = 1ll * x * x % MOD;
    y >>= 1;
  }
  return ret;
}
inline void Add(int &x, const int y) { ((x += y) >= MOD) && (x -= MOD); }
signed main() {
  read(n, k);
  f[0] = 1;
  for (int i = (1); i <= (n); ++i) {
    const int x = read();
    for (int j = (i); j >= (1); --j)
      f[j] = (1ll * f[j] * x - f[j - 1] + MOD) % MOD;
    f[0] = 1ll * f[0] * x % MOD;
  }
  const int inv = ksm(n, MOD - 2);
  int ans = 0, cur = 1;
  for (int j = (0); j <= (n); ++j) {
    Add(ans, 1ll * f[j] * cur % MOD);
    cur = 1ll * cur * inv % MOD * (k - j) % MOD;
  }
  print((f[0] - ans + MOD) % MOD);
}

```