The Golomb sequence $G_1, G_2, \ldots$ is a non-decreasing integer sequence such that for each positive integer $n$, $G_n$ is the number of occurrences of $n$ in this sequence. The first few elements of $G$ are $[1, 2, 2, 3, 3, 4, 4, 4, 5, \ldots]$. Do you know the recurrence relation for the Golomb sequence? It is $G_1 = 1$ and $G_{n+1} = 1+G_{n+1-G_{G_n}}$ for each $n \ge 1$. A self-describing sequence, isn't it?
Mr. Strange wants to learn CP, so he asked Chef, who is one of the best competitive programmers in the world, to teach him. Chef decided to test his ability by giving him the following task.
Find the sum of squares of the $L$-th through $R$-th term of the Golomb sequence, i.e. $S = \sum_{i=L}^R G_i^2$. Since the sum can be quite large, compute it modulo $10^9+7$.
Can you help Mr. Strange carry out this task given to him by his teacher?

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains two space-separated integers $L$ and $R$.

-----Output-----
For each test case, print a single line containing one integer $S$ modulo $10^9+7$.

-----Constraints-----
- $1 \le T \le 10^5$
- $1 \le L \le R \le 10^{10}$

-----Subtasks-----
Subtask #1 (50 points):
- $T \le 10^2$
- $R \le 10^9$
Subtask #2 (50 points): original constraints

-----Example Input-----
3
1 5
2 4
100 100

-----Example Output-----
27
17
441

-----Explanation-----
Example case 1: $1^2 + 2^2 + 2^2 + 3^2 + 3^2 = 27$
Example case 2: $2^2 + 2^2 + 3^2 = 17$
Example case 3: $21^2 = 441$

```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 = 'def find_upper_bound(arr,key):\n low,high = 0,len(arr)-1\n while low<=high:\n  mid = (low+high)//2 \n  if arr[mid]==key:return mid\n  elif arr[mid]>key and mid-1>=0 and arr[mid-1]<key:return mid \n  elif arr[mid]>key:high = mid - 1 \n  else:low = mid + 1 \n return mid \ndef get_query(l):\n nonlocal prefix_storer,bin_storer\n ind = find_upper_bound(bin_storer,l)\n surplus = (abs(bin_storer[ind]-l)*ind*ind)%limit \n return (prefix_storer[ind]-surplus+limit)%limit\ndef fire_query(l,r):\n return (get_query(r)-get_query(l-1)+limit)%limit\ngolomb,dp,prefix_storer,bin_storer = [],[0,1],[0,1],[0,1]\nlimit = 10**9+7\nfor i in range(2,10**6+100):\n dp.append(1 + dp[i-dp[dp[i-1]]])\n bin_storer.append(dp[-1]+bin_storer[-1])\n prefix_storer.append(((prefix_storer[-1] + (dp[-1]*i*i)%limit))%limit)\n# print(dp[1:20])\n# print(bin_storer[1:20])\n# print(prefix_storer[1:20])\n# print(get_query(2),get_query(4))\nfor _ in range(int(input())):\n l,r = map(int,input().split())\n print(fire_query(l,r))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: