Count Dice Sequences

A standard die produces an integer from 1 through 6. Count all nonempty ordered sequences of outcomes whose sum is target. Different orders count separately. Return the count modulo 1,000,000,007.

Implement dice_combinations(target).

Input

target: The required sum of all rolls.

Output

Return the number of sequences modulo 1,000,000,007.

Constraints

1 ≤ target ≤ 1,000,000. Taking a count modulo 1,000,000,007 means returning its remainder after division by that number.

Examples

Input:
target = 2

Expected output:
expected = 2

Input:
long long target = 2;

Expected output:
long long expected = 2;

Input:
long target = 2;

Expected output:
long expected = 2;

Input:
target = 4

Expected output:
expected = 8

Input:
long long target = 4;

Expected output:
long long expected = 8;

Input:
long target = 4;

Expected output:
long expected = 8;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Dice Combinations — 1633