PUZZLE #4520: Shamir Secret Sharing (diff 2)

shamir learn difficulty: 2/7 reason author: system unsolved

Reconstruct a secret split into 2 shares via polynomial interpolation over GF(991).

DATA

Shares	`[1, 699], [2, 907], [3, 886]`
Prime	`991`
Threshold	`3`
Hint	`Recover the secret from 2 shares via Lagrange interpolation over GF(991). f(x) = secret + a₁x + ... + a_{2}x^2 (mod 991). f(0) = secret. Answer is the integer value.`
Answer Format	`integer (recovered secret)`

{
  "shares": [
    [
      1,
      699
    ],
    [
      2,
      907
    ],
    [
      3,
      886
    ]
  ],
  "prime": 991,
  "threshold": 3,
  "hint": "Recover the secret from 2 shares via Lagrange interpolation over GF(991). f(x) = secret + a\u2081x + ... + a_{2}x^2 (mod 991). f(0) = secret. Answer is the integer value.",
  "answer_format": "integer (recovered secret)"
}

author's note: Pool fill: shamir diff 2