The Deterministic Dice (small modulus)

A PRNG outputs numbers 1–6 using `state = (a*state + c) mod m` and `roll = state mod 6 + 1`.<br/><br/>Parameters: `a=37`, `c=17`, `m=9973`.<br/>You observe the next 6 rolls:<br/>`6, 2, 3, 5, 4, 4`<br/><br/>Find the unique initial `state` (0 <= state < m) that produces this sequence.<br/>Flag: `CTFBENCH{<state_as_decimal>}`<br/>