Given an array of integers A, consider all non-empty subsequences of A.
For any sequence S, let the width of S be the difference between the maximum and minimum element of S.
Return the sum of the widths of all subsequences of A. 
As the answer may be very large, return the answer modulo 10^9 + 7.

 
Example 1:
Input: [2,1,3]
Output: 6
Explanation:
Subsequences are [1], [2], [3], [2,1], [2,3], [1,3], [2,1,3].
The corresponding widths are 0, 0, 0, 1, 1, 2, 2.
The sum of these widths is 6.

 
Note:

1 <= A.length <= 20000
1 <= A[i] <= 20000

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from bisect import bisect_left, bisect_right\n\nclass Solution:\n    def sumSubseqWidths(self, A: List[int]) -> int:\n        n = len(A)\n        ret = 0\n        \n        # F[i] number of subsequences accept A[i] as minimun\n        # G[i] number of subsequences accept A[i] as maximum\n        # result = (-F[i] + G[i]) * A[i]        \n        \n        \n        A.sort()   \n        MOD = 10 ** 9 + 7\n        \n        @lru_cache\n        def bimod(n):\n            if n == 0:\n                return 1\n            di = bimod(n // 2)\n            if n % 2 == 0:\n                return di * di % MOD\n            return di * di * 2 % MOD\n        \n        @lru_cache\n        def nonempty(n):\n            return bimod(n) - 1\n        \n        i = 0\n        while i < n:\n            j = i\n            while j < n and A[j] == A[i]:\n                j+=1\n            se = j - i\n            sl = i\n            sr = n-j\n            \n            # ret = (ret + (2**sl-1) * (2**se-1) * A[i] % MOD) % MOD\n            # ret = (ret - (2**sr-1) * (2**se-1) * A[i] % MOD) % MOD\n            ret = (ret + A[i] * nonempty(se) * (nonempty(sl) - nonempty(sr)) % MOD) % MOD\n            i = j\n        \n        return ret % MOD\n        \n\n            \n            \n    \n            \n            \n            \n            \n            \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'sumSubseqWidths'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 9366