The description is rather long but it tries to explain what a financing plan is. 

The fixed monthly payment for a fixed rate mortgage is the amount paid by the borrower every month that ensures 
that the loan is paid off in full with interest at the end of its term. 

The monthly payment formula is based on the annuity formula. 
The monthly payment `c` depends upon:

- `rate` - the monthly interest rate is expressed as a decimal, not a percentage. 
The monthly rate is simply the **given** yearly percentage rate divided by 100 and then by 12.

- `term` - the number of monthly payments, called the loan's `term`.
- `principal` - the amount borrowed, known as the loan's principal (or `balance`).

First we have to determine `c`.

We have: `c = n /d` with `n = r * balance` and `d = 1 - (1 + r)**(-term)` where `**` is the `power` function (you can look at the reference below).

The payment `c` is composed of two parts. The first part pays the interest (let us call it `int`)
due for the balance of the given month, the second part repays the balance (let us call this part `princ`) hence for the following month we get a `new balance = old balance - princ` with `c = int + princ`. 

Loans are structured so that the amount of principal returned to the borrower starts out small and increases with each mortgage payment. 
While the mortgage payments in the first years consist primarily of interest payments, the payments in the final years consist primarily of principal repayment.

A mortgage's amortization schedule provides a detailed look at precisely what portion of each mortgage payment is dedicated to each component.

In an example of a $100,000, 30-year mortgage with a rate of 6 percents the amortization schedule consists of 360 monthly payments.
The partial amortization schedule below shows with 2 decimal floats
the balance between principal and interest payments.

--|num_payment|c          |princ      |int        |Balance    |
--|-----------|-----------|-----------|-----------|-----------|
--|1          |599.55     |99.55      |500.00     |99900.45   |
--|...        |599.55     |...        |...        |...        |
--|12         |599.55     |105.16     |494.39     |98,771.99  |
--|...        |599.55     |...        |...        |...        |
--|360        |599.55     |596.57     |2.98       |0.00       |

# Task:
Given parameters 
```
rate: annual rate as percent (don't forgent to divide by 100*12)
bal: original balance (borrowed amount) 
term: number of monthly payments
num_payment: rank of considered month (from 1 to term)
```
the function `amort` will return a formatted string:

`"num_payment %d c %.0f princ %.0f int %.0f balance %.0f" (with arguments num_payment, c, princ, int, balance`)

# Examples:
```
amort(6, 100000, 360, 1) ->
"num_payment 1 c 600 princ 100 int 500 balance 99900"

amort(6, 100000, 360, 12) ->
"num_payment 12 c 600 princ 105 int 494 balance 98772"

```
# Ref

```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 = 'amort=lambda r,b,t,n,c=0,p=0,i=0,m=-1:m<0and amort(r/1200,b,t,n,r/1200*b/(1-(1+r/1200)**-t),p,i,0)or m==n and"num_payment %d c %.0f princ %.0f int %.0f balance %.0f"%(n,c,p,i,b)or amort(r,r*b+b-c,t-1,n,c,c-r*b,r*b,m+1)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'amort'
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: 12899