Given an array of integers arr. Return the number of sub-arrays with odd sum.
As the answer may grow large, the answer must be computed modulo 10^9 + 7.
 
Example 1:
Input: arr = [1,3,5]
Output: 4
Explanation: All sub-arrays are [[1],[1,3],[1,3,5],[3],[3,5],[5]]
All sub-arrays sum are [1,4,9,3,8,5].
Odd sums are [1,9,3,5] so the answer is 4.

Example 2:
Input: arr = [2,4,6]
Output: 0
Explanation: All sub-arrays are [[2],[2,4],[2,4,6],[4],[4,6],[6]]
All sub-arrays sum are [2,6,12,4,10,6].
All sub-arrays have even sum and the answer is 0.

Example 3:
Input: arr = [1,2,3,4,5,6,7]
Output: 16

Example 4:
Input: arr = [100,100,99,99]
Output: 4

Example 5:
Input: arr = [7]
Output: 1

 
Constraints:

1 <= arr.length <= 10^5
1 <= arr[i] <= 100

```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 = 'class Solution:\n    # brute force：把所有的substring都for一遍，可以用bit operation优化\n    # 其实不用两个数相加再整除2，直接看最后一位是不是1就行，可以用xor代替相加\n    # better approach：对于每个index i，维护evens和odds，分别是在i之前的even prefix sum和odd prefix sum数量，然后用位运算优化\n    def numOfSubarrays(self, arr: List[int]) -> int:\n        n = len(arr)\n        ret = 0\n        # 当前是odd和是even的prefix sums个数\n        odds, evens = 0, 1\n        cur = 0 # 当前的prefix sum\n        \n        for num in arr:\n            cur ^= num&1    # 查看奇偶\n            if cur:         # 奇数\n                # 如果当前prefix sum是奇数，查看在此之前有多少个偶数的prefix sum\n                # 用cur减去之前所有是偶数的prefix sum，都可以得到一段奇数的substring\n                ret += evens\n                odds += 1\n            else:\n                # vice versa\n                ret += odds\n                evens += 1\n        \n        return ret % (10**9 + 7)\n        \n        \n#     def numOfSubarrays(self, arr: List[int]) -> int:\n#         n = len(arr)\n#         ret = 0\n        \n#         presum = [0 for i in range(n)]\n#         for i in range(n):\n#             presum[i] = (arr[i] + (presum[i-1] if i > 0 else 0))&1\n        \n#         for i in range(n):\n#             for j in range(i, n):\n#                 if i == j:\n#                     if arr[i]&1: ret += 1\n#                 elif not i:\n#                     if presum[j]: ret += 1\n#                 else:\n#                     if presum[j]^presum[i-1]: ret += 1\n\n#         return ret\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numOfSubarrays'
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: 5392