1. Abridged Problem Statement  
Given two integers N (day) and M (month) for a date in the year 2001, output the weekday number (Monday=1, …, Sunday=7). If the date is invalid (e.g., month not in 1–12 or day exceeds that month’s length in 2001), print “Impossible”.

2. Detailed Editorial  
We know that January 1, 2001, was a Monday. To find the weekday of any date N M in 2001:
  • First, validate M is in [1..12] and N is in [1..days_in_month[M]]. If not, answer is “Impossible.”  
  • Otherwise, compute the total number of days elapsed from January 1 to the given date, call it D (0 for Jan 1, 1 for Jan 2, …).  
    – Let days_in_month = [31,28,31,30,31,30,31,31,30,31,30,31].  
    – Set D = (sum of days in months 1 through M–1) + (N–1).  
  • The weekday index is then (D mod 7) + 1, since D=0 → Monday=1, …, D=6 → Sunday=7, then it repeats.  
This runs in O(1) time and constant space.

3. C++ Solution with Detailed Comments  
#include <bits/stdc++.h>  
using namespace std;

// Predefined lengths of each month in 2001 (not a leap year)
vector<int> months = {31,28,31,30,31,30,31,31,30,31,30,31};

int n, m;

// Read input N and M
void read() {
    cin >> n >> m;
}

// Solve and print result
void solve() {
    // Check for invalid month or day
    if (m < 1 || m > 12 || n < 1 || n > months[m - 1]) {
        cout << "Impossible\n";
        return;
    }
    // Convert to zero-based day offset from Jan 1
    int D = 0;
    // Add days from all preceding months
    for (int i = 1; i < m; i++) {
        D += months[i - 1];
    }
    // Add days within current month, shifting Jan 1 to D=0
    D += (n - 1);
    // Weekday: D=0 → Monday=1, …, D mod 7 + 1
    int weekday = (D % 7) + 1;
    cout << weekday << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);

    read();
    solve();
    return 0;
}

4. Python Solution with Detailed Comments  
```python
import sys

def main():
    data = sys.stdin.read().split()
    if len(data) < 2:
        return
    n, m = map(int, data)       # n = day, m = month

    # Month lengths in 2001 (non-leap year)
    months = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

    # Validate input
    if m < 1 or m > 12 or n < 1 or n > months[m - 1]:
        print("Impossible")
        return

    # Compute days elapsed since Jan 1 (zero-based)
    days_elapsed = sum(months[:m - 1]) + (n - 1)

    # Monday=1, …, Sunday=7
    weekday = (days_elapsed % 7) + 1
    print(weekday)

if __name__ == "__main__":
    main()
```

5. Compressed Editorial  
Compute D = sum of days in months before M plus (N–1). If M∉[1..12] or N>month_length[M], print “Impossible”. Else output (D mod 7)+1, since Jan 1, 2001 is Monday (D=0→1).