[INSTRUCTIONS]

You are a program-analysis assistant. Your task is to statically analyze the control dependence of a given code snippet. 

## 1. Control Dependence Definition
  Control dependence captures the influence of control-flow decisions on the execution of statements.

  A statement `S2` is control-dependent on `S1` if there is a **transitive** (indirect) chain of **direct** control dependencies from `S1` to `S2`. This is equivalent to saying that `S1` has control dependence over `S2`, meaning `S1`’s condition influences whether `S2` executes.


  **Direct Control Dependence**:
  A statement `S2` is **directly** control-dependent on a statement `S1` if:
  
  1.	`S1` is a conditional control statement (e.g., an `if`, `while`, `for`, `switch`, etc.).
  
  2.	`S1` directly determines whether `S2` executes. That is, `S1` has multiple successor branches, 

  - there exists **at least one branch** in which `S2` **always executes**, and
  - there exists **at least one other branch** in which `S2` does **not necessarily execute**.

    “Not necessarily execute” means that `S2` might execute or might not, but it is **not guaranteed** to execute in that branch.

  `S2` is **control-dependent** on `S1` if there exists a **transitive chain** of control dependencies from `S1` to `S2`, where each intermediate step in the chain represents a **direct** control dependence between two statements.



## 2. Output Format
When asked, “Does line `S1` have control dependence over line `S2`? If so, provide a trace.” You should respond in JSON format as follows:

- If there is a control dependence:

```json
{
  "ControlDependence": true,
  "Trace": [S1, ..., S2]
}
```

- If there is no control dependence:
```json
{
  "ControlDependence": false
}
```

A **trace** represents a **transitive control flow**, where each adjacent pair in the list reflects a **direct** control dependence. The trace must starts with `S1` and ends with `S2`.


    

## 3. Interprocedural Control Dependence
  All dependence analysis is performed within **a single function**. We do not track dependencies across function boundaries. The analysis only applies to variables and control structures inside the **specified function**.


## 4. Example Code Snippet

### Example 1

```python
1  if x > 0:
2      y = 10       # this line is directly control-dependent on line 1 (x>0)
3      if y > 5:
4          z = 20   # this line is directly control-dependent on line 3 (y>5)
5          w = 30   # this line is directly control-dependent on line 3 (y>5)
6  v = 40           # this line is NOT control-dependent on any line
```


**Analysis**:
- Line 2 is directly control-dependent on line 1 (`x>0`)
- Lines 4 and 5 are directly control-dependent on line 3 (`y>5`).
- Lines 4 and 5 are **indirectly** control-dependent on line 1 (`x>0`) becasue even if line 1 (`x>0`) is `true`, lines 4 and 5 may not execute if line 3’s condition (`y>5`) is `false`. However, since control dependence is transitive, lines 4 and 5 are **indirectly** control-dependent on line 1. 
- Line 6 is not control-dependent on any lines because Line 6 always executes, regardless of whether line 1 (`x>0`) or line 3 (`y>5`) is true or false.



#### Example Question 1.1: 
Does line `1` have control dependence over line `5`? If so, provide a trace.

**Output**: 
```json
{
  "ControlDependence": true,
  "Trace": [1, 3, 5]
}
```

#### Example Question 1.2:
Does line `3` have control dependence over line `6`? If so, provide a trace.

**Output**: 
```json
{
  "ControlDependence": false
}
```


### Example 2

```python
1  count = 0
2  if count < 5:
3      count += 1
4  print("Step 1 done")
5  while count < 10:
6      if count == 7:
7          break
8      if count % 2 == 0:
9          continue
10     count += 2
11     if count > 9:
12         count = 9
13     print("Iteration done")
14 print("End of program")
```

#### Example Question 2.1: 
Does line `5` have control dependence over line `13`? If so, provide a trace.

**Analysis**:
  - Line 13 is directly control-dependent on line 8 because if line 8 evaluates to `true`, continue skips line 13 for that iteration.
  - Line 8 is directly control-dependent on line 6 because if line 6 evaluates to `true`, the break statement terminates the loop, preventing line 8 from executing.
  - Line 6 is directly control-dependent on line 5 because the loop condition at line 5 determines whether line 6 executes. If line 5 evaluates to `false`, execution skips the loop entirely.


Since control dependence is transitive, line 5 indirectly controls line 13 through lines 6 and 8. The trace is `5->6->8->13`.

**Output**:
```json
{
  "ControlDependence": true,
  "Trace": [5, 6, 8, 13]
}
```

#### Example Question 2.2: 
Does line `8` have control dependence over line `10`? If so, provide a trace.


**Analysis**: Similar to the explanation above, line 8 is an `if` condition inside the `while` loop with a `continue`, so it can make the execution skip the rest of the loop entirely, including line 10. Therefore, line 10 directly control-dependent on 8.



**Output**:
```json
{
  "ControlDependence": true,
  "Trace": [8, 10]
}
```

#### Example Question 2.3: 
Does line `5` have control dependence over line `14`? If so, provide a trace.

**Analysis**: Line 5 doesn't affect whether line 14 is reached. Line 14 is outside the while loop (lines 5 -- 13) and will be executed regardless of the condition. 

**Output**:
```json
{
  "ControlDependence": false
}
```


#### Example Question 2.4: 
Does line `2` have control dependence over line `12`? If so, provide a trace.

**Analysis**: Line 2 doesn't affect whether line 12 is reached. The condition in line 2 only controls whether line 3 is executed. Line 12 is in while loop (line 5 -- 13) and will or will not be executed regardless of the condition in line 2. 

**Output**:
```json
{
  "ControlDependence": false
}
```

---

[YOUR TURN]

Below is **your target snippet**. 

```Python
1   import sys,math,collections
2   from collections import defaultdict
3   def file():
4       sys.stdin = open('input.py', 'r')
5       sys.stdout = open('output.py', 'w') 
6   def get_array():
7       l=list(map(int, input().split()))
8       return l
9   def get_ints():   
10      return map(int, input().split())
11  def get_3_ints():   
12      a,b,c=map(int, input().split())
13      return a,b,c    
14  def sod(n):
15      n,c=str(n),0
16      for i in n: 
17          c+=int(i)
18      return c    
19  def isPrime(n):
20      if (n <= 1):
21          return False
22      if (n <= 3):
23          return True
24      if (n % 2 == 0 or n % 3 == 0):
25          return False
26      i = 5
27      while(i * i <= n):
28          if (n % i == 0 or n % (i + 2) == 0):
29              return False
30          i = i + 6
31      return True
32  def getFloor(A, x):
33      (left, right) = (0, len(A) - 1)
34      floor = -1
35      while left <= right:
36          mid = (left + right) // 2
37          if A[mid] == x:
38              return A[mid]
39          elif x < A[mid]:
40              right = mid - 1
41          else:
42              floor = A[mid]
43              left = mid + 1
44      return floor
45  def chk(aa,bb):
46  	f=0
47  	for i in aa:
48  		for j in bb:
49  			if(j[0]>=i[0] and j[1]<=i[1]):
50  				f+=1
51  			elif(j[0]<=i[0] and j[1]>=i[1]):	
52  				f+=1
53  			elif(i[0]==j[1] or i[1]==j[0]):
54  				f+=1
55  			else:
56  				continue
57  	return f	
58  def maxSumRangeQuery(nums, req):
59      l = []
60      for _ in range(len(nums)+1):
61          l.append(0)
62      nums.sort(reverse=True)
63      for i in req:
64          l[i[0]]+=1
65          l[i[1]+1]-=1
66      for i in range(1,len(l)):
67          l[i]+=l[i-1]
68      l=l[:-1]    
69      d=collections.defaultdict(list)
70      for i in range(len(l)):
71          d[l[i]].append(i)
72      di=collections.OrderedDict(sorted(d.items()))   
73      k=0
74      ans = []
75      for _ in range(len(nums)):
76          ans.append(0)
77      for i in di:
78          for j in di[i]:
79              ans[j]=nums[len(nums)-k-1]
80              k+=1
81      c=0
82      for i in req:
83          st=ans[i[0]:i[1]+1]
84          c+=sum(st)
85      return c%(10**9+7)
86  def main():
87  	c=0
88  	a,b=get_ints()
89  	while(a>0):
90  		a-=b
91  		c+=1
92  	print(c)	
93  if __name__ == '__main__':
94      main()
```


**Question**: Does line `78` have control dependence over line `79` in function `maxSumRangeQuery`? If so, provide a trace.

**Output**:


Ground truth answer: yes