G. LCM-er

Codeforces

IDCF10113G

Time2000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

You are given four integers n, a, b and x. Your task is to count modulo 109 + 7 the number of sequences of integers A satisfying the following conditions: The only line of the input contains four integers n, a, b and x (1 ≤ n ≤ 100, 1 ≤ a, b, x ≤ 109, a ≤ b). Count sequences of integers satisfying the given conditions. Print the answer modulo 109 + 7. In the first sample there are 9 valid sequences: (1, 6), (2, 3), (2, 6), (3, 4), (3, 6), (4, 6), (5, 6), (6, 6), (6, 7). ## Input The only line of the input contains four integers n, a, b and x (1 ≤ n ≤ 100, 1 ≤ a, b, x ≤ 109, a ≤ b). ## Output Count sequences of integers satisfying the given conditions. Print the answer modulo 109 + 7. [samples]

**Definitions** Let $ n, a, b, x \in \mathbb{Z} $ be given integers with $ 1 \leq n \leq 100 $, $ 1 \leq a \leq b $, $ 1 \leq x \leq 10^9 $. Let $ A = (A_1, A_2, \dots, A_n) $ be a sequence of integers. **Constraints** 1. $ a \leq A_i \leq b $ for all $ i \in \{1, \dots, n\} $ 2. $ \gcd(A_1, A_2, \dots, A_n) = x $ **Objective** Count the number of such sequences $ A $ modulo $ 10^9 + 7 $.

API Response (JSON)

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      "content": "You are given four integers n, a, b and x. Your task is to count modulo 109 + 7 the number of sequences of integers A satisfying the following conditions: The only line of the input contains four int",
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