# Polo the Penguin and the Numbers | codechef solution

Polo, the Penguin, likes numbers. He says that the goodness of a number is itself multiplied by the number of digits in it's decimal representation. For example, the goodness of the integer 474 is 474*3 = 1422.

Help him to count the sum of goodness of all integers from L to R, inclusive. Since the answer can be too large, output it modulo 1,000,000,007 (10^9+7).

### Input

The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. The only line of each test case contains the pair of integers L and R, separated by a single space.

### Output

For each test case, output a single line containing the answer to the corresponding test case.

### Constraints

• 1 ≤ T ≤ 1,000
• 1 ≤ L ≤ R ≤ 1,000,000,000 (10^9)

Input
Output
```1
9 12```
`75`

### Explanation:

Example case 1. The answer is 9*1 + 10*2 + 11*2 + 12*2 = 75.

Code(C++):-

#include <bits/stdc++.h>
using namespace std;
#define ull long long int
#define m (ull)(1000000007)

int main()
{
int t;
cin >> t;
while (t--)
{
int l, r;
cin >> l >> r;
int dl = to_string(l).size(), dr = to_string(r).size();
ull S = 0;
while (dl <= dr)
{
ull a = max(l, (int)pow(10, (dl - 1))), an = min((int)((ull)pow(10, dl) - 1), r);
ull s1 = (an - a + 1), s2 = (a + an), s = 0;
s = (s1 % 2 == 0 ? ((s1 / 2) * s2 * dl) : ((s2 / 2) * s1 * dl));
S += (s % m);
S %= m;
dl++;
}
cout << S << "\n";
}
return 0;
}

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