Chef is given a sequence of prime numbers $A_1, A_2, \ldots, A_N$. This sequence has exactly $2^N$ subsequences. A subsequence of $A$ is good if it does not contain any two identical numbers; in particular, the empty sequence is good.
Chef has to find the number of good subsequences which contain at most $K$ numbers. Since he does not know much about subsequences, help him find the answer. This number could be very large, so compute it modulo $1,000,000,007$.

-----Input-----
- The first line of the input contains two space-separated integers $N$ and $K$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
Print a single line containing one integer ― the number of good subsequences with size at most $K$, modulo $1,000,000,007$.

-----Constraints-----
- $1 \le K \le N \le 10^5$
- $2 \le A_i \le 8,000$ for each valid $i$

-----Subtasks-----
Subtask #1 (40 points): $A_1, A_2, \ldots, A_N$ are pairwise distinct
Subtask #2 (60 points): original constraints

-----Example Input-----
5 3
2 2 3 3 5

-----Example Output-----
18

-----Explanation-----
There is $1$ good subsequence with length $0$, $5$ good subsequences with length $1$, $8$ good subsequences with length $2$ and $4$ good subsequences with length $3$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '\ndef compute_coeff(roots,k):\n mod = 10**9+7\n res = [1 for i in range(len(roots)+1) ]\n for i in range(len(roots)):\n  cur_root = roots[i]\n  for j in range(i,-1,-1):\n   if j==0:res[j] *= -cur_root\n   else:res[j] = res[j-1] - res[j]*cur_root\n   if res[j] >=mod:res[j] %=mod\n for i in range(len(res)):res[i] = (abs(res[i])%mod)\n return res\nn,k = map(int,input().split())\narr = list(map(int,input().split()))\nd,a = dict(),0\nfor i in arr:\n if i not in d.keys():d[i] = 1\n else:d[i] += 1\nans = compute_coeff(list(d.values()),k)\nans = ans[::-1]\nprint(sum(ans[:k+1])%(10**9+7))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13365