The Binomial Form of a polynomial has many uses, just as the standard form does.  For comparison, if p(x) is in Binomial Form and q(x) is in standard form, we might write

p(x) := a0 \* xC0 + a1 \* xC1 + a2 \* xC2 + ... + aN \* xCN

q(x) := b0 + b1 \* x + b2 \* x^(2) + ... + bN \* x^(N)

Both forms have tricks for evaluating them, but tricks should not be necessary.  The most important thing to keep in mind is that aCb can be defined for non-integer values of a; in particular,

```
aCb := a * (a-1) * (a-2) * ... * (a-b+1) / b!   // for any value a and integer values b
    := a! / ((a-b)!b!)                          // for integer values a,b
```

The inputs to your function are an array which specifies a polynomial in Binomial Form, ordered by highest-degree-first, and also a number to evaluate the polynomial at.  An example call might be

```python
value_at([1, 2, 7], 3)
```

and the return value would be 16, since 3C2 + 2 * 3C1 + 7 = 16.  In more detail, this calculation looks like

```
1 * xC2 + 2 * xC1 + 7 * xC0 :: x = 3
3C2 + 2 * 3C1 + 7
3 * (3-1) / 2! + 2 * 3 / 1! + 7
3 + 6 + 7 = 16
```

More information can be found by reading about [Binomial Coefficients](https://en.wikipedia.org/wiki/Binomial_coefficient) or about [Finite Differences](https://en.wikipedia.org/wiki/Finite_difference).

Note that while a solution should be able to handle non-integer inputs and get a correct result, any solution should make use of rounding to two significant digits (as the official solution does) since high precision for non-integers is not the point here.

```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 = 'def value_at(poly_spec, x):\n    if len(poly_spec) < 2: return poly_spec[0] if poly_spec else 0\n    l = len(poly_spec) - 1\n    m = [co * binomial(x, l - i) for i, co in enumerate(poly_spec[:-1])]\n    return round(float(sum(m) + poly_spec[l]), 2)\n    \ndef factorial(n):\n    return 1 if n < 2 else n * factorial(n - 1)\n    \ndef binomial(a, b): \n    res = 1.0\n    for k in range(b): res *= (a - k)\n    return res / factorial(b)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'value_at'
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: 6598