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m-Beautiful Numbers

By moshiur_cse15 · Limits 3s, 512 MB

An m-Beautiful Number is a number which is divisible by $m$ and the sum of the digits is also divisible by $m$. For example, $268$ is a 4-Beautiful Number, but $68$ and $26$ are not 4-Beautiful Number.

In this problem, you'll be given $3$ integers, $L$, $R$, and $m$, and you have to tell the number of m-Beautiful Numbers in between L and R (inclusive) . As the answer can be very large, you have to print it modulo $10^9 + 7$.

Input

The first line of the input will contain a number $T$ ($1 ≤ T ≤ 10^5$), number of test cases to follow. Next $T$ lines will contain $3$ integers $L$, $R$ ($1 ≤ L ≤ R ≤ 10^{50}$), and $m$ ($1 ≤ m ≤ 50$) each as stated in description.

Output

For each case, you have to print the number of m-Beautiful Numbers in between $L$ and $R$ (inclusive) modulo $10^9 + 7$.

Sample

InputOutput
2
1 20 3
1 20 4
6
2

3-Beautiful Numbers between $1$ to $20$: $3$, $6$, $9$, $12$, $15$, and $18$.

4-Beautiful Numbers between $1$ to $20$: $4$, and $8$.


Discussion

Statistics


39% Solution Ratio

dip_BRUREarliest, Dec '19

EgorKulikovFastest, 0.9s

dip_BRURLightest, 18 MB

steinumShortest, 1086B

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