Dice Combinations

MOD = 10**9 + 7

def count_ways_to_sum(n):
    # DP array to store the number of ways to form sum i
    dp = [0] * (n + 1)
    dp[0] = 1  # There's 1 way to form sum 0 (doing nothing)

    window_sum = dp[0]  # This will hold the sum of the last six dp values

    for i in range(1, n + 1):
        # Calculate dp[i] based on the running sum of the last six values
        dp[i] = window_sum % MOD
        
        # Update the sliding window sum
        window_sum = (window_sum + dp[i]) % MOD

        # If we are past the first six elements, subtract dp[i-6]
        if i >= 6:
            window_sum = (window_sum - dp[i - 6]) % MOD

    return dp[n]

# Input
n = int(input())

# Output
print(count_ways_to_sum(n))

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED