[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**. 

```Java
1   import java.util.Arrays;
2   import java.util.Scanner;
3   public class Main {
4       Scanner   sc2   = new Scanner(System.in);
5       long      start = System.currentTimeMillis();
6       long      fin   = System.currentTimeMillis();
7       final int MOD   = 1000000007;
8       int[]     dx    = { 1, 0, 0, -1 };
9       int[]     dy    = { 0, 1, -1, 0 };
10      void run() {
11          MyScanner sc    = new MyScanner();
12          int n = sc.nextInt();
13          int m = sc.nextInt();
14          int M = 998244353;
15          if (m > 200000) {
16              return;
17          }
18          int[][] dp = new int[2][m];
19          int[] sum = new int[m];
20          dp[0][0] = 1;
21          dp[0][1] = 1;
22          sum[0] = 1;
23          sum[1] = 2;
24          for (int i = 2; i < m; i++) {
25              dp[0][i] = (dp[0][i - 1] + dp[0][i - 2]) % M;
26              sum[i] = (sum[i - 1] + dp[0][i]) % M;
27          }
28          long last = dp[0][m - 1];
29          for (int i = 1; i < n; i++) {
30              int[] next = new int[m];
31              next[0] = sum[0];
32              for (int j = 1; j < m; j++) 
33                  next[j] = (next[j - 1] + sum[j]) % M;
34              last = sum[m - 1];
35              sum = next;
36          }
37          System.out.println(last);
38      }
39      public static void main(String[] args) {
40          new Main().run();
41      }
42      void debug(Object... o) {
43          System.out.println(Arrays.deepToString(o));
44      }
45      void debug2(int[][] array) {
46          for (int i = 0; i < array.length; i++) {
47              for (int j = 0; j < array[i].length; j++) {
48                  System.out.print(array[i][j]);
49              }
50              System.out.println();
51          }
52      }
53      boolean inner(int h, int w, int limH, int limW) {
54          return 0 <= h && h < limH && 0 <= w && w < limW;
55      }
56      void swap(int[] x, int a, int b) {
57          int tmp = x[a];
58          x[a] = x[b];
59          x[b] = tmp;
60      }
61      int lower_bound(int a[], int k) {
62          int l = -1;
63          int r = a.length;
64          while (r - l > 1) {
65              int mid = (l + r) / 2;
66              if (k <= a[mid])
67                  r = mid;
68              else
69                  l = mid;
70          }
71          return r;
72      }
73      int upper_bound(int a[], int k) {
74          int l = -1;
75          int r = a.length;
76          while (r - l > 1) {
77              int mid = (l + r) / 2;
78              if (k < a[mid])
79                  r = mid;
80              else
81                  l = mid;
82          }
83          return r;
84      }
85      long gcd(long a, long b) {
86          return a % b == 0 ? b : gcd(b, a % b);
87      }
88      long lcm(long a, long b) {
89          return a * b / gcd(a, b);
90      }
91      boolean palindrome(String s) {
92          for (int i = 0; i < s.length() / 2; i++) {
93              if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
94                  return false;
95              }
96          }
97          return true;
98      }
99      class MyScanner {
100          int nextInt() {
101              try {
102                  int c = System.in.read();
103                  while (c != '-' && (c < '0' || '9' < c))
104                      c = System.in.read();
105                  if (c == '-')
106                      return -nextInt();
107                  int res = 0;
108                  do {
109                      res *= 10;
110                      res += c - '0';
111                      c = System.in.read();
112                  } while ('0' <= c && c <= '9');
113                  return res;
114              } catch (Exception e) {
115                  return -1;
116              }
117          }
118          double nextDouble() {
119              return Double.parseDouble(next());
120          }
121          long nextLong() {
122              return Long.parseLong(next());
123          }
124          String next() {
125              try {
126                  StringBuilder res = new StringBuilder("");
127                  int c = System.in.read();
128                  while (Character.isWhitespace(c))
129                      c = System.in.read();
130                  do {
131                      res.append((char) c);
132                  } while (!Character.isWhitespace(c = System.in.read()));
133                  return res.toString();
134              } catch (Exception e) {
135                  return null;
136              }
137          }
138          int[] nextIntArray(int n) {
139              int[] in = new int[n];
140              for (int i = 0; i < n; i++) {
141                  in[i] = nextInt();
142              }
143              return in;
144          }
145          int[][] nextInt2dArray(int n, int m) {
146              int[][] in = new int[n][m];
147              for (int i = 0; i < n; i++) {
148                  in[i] = nextIntArray(m);
149              }
150              return in;
151          }
152          double[] nextDoubleArray(int n) {
153              double[] in = new double[n];
154              for (int i = 0; i < n; i++) {
155                  in[i] = nextDouble();
156              }
157              return in;
158          }
159          long[] nextLongArray(int n) {
160              long[] in = new long[n];
161              for (int i = 0; i < n; i++) {
162                  in[i] = nextLong();
163              }
164              return in;
165          }
166          char[][] nextCharField(int n, int m) {
167              char[][] in = new char[n][m];
168              for (int i = 0; i < n; i++) {
169                  String s = sc.next();
170                  for (int j = 0; j < m; j++) {
171                      in[i][j] = s.charAt(j);
172                  }
173              }
174              return in;
175          }
176      }
177  }
```


**Question**: Does line `29` have control dependence over line `35` in function `run`? If so, provide a trace.

**Output**:


Ground truth answer: yes