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B. Strip

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAlexandra has a paper strip with *n* numbers on it. Let's call them *a*_{i} from left to right.

Now Alexandra wants to split it into some pieces (possibly 1). For each piece of strip, it must satisfy:

Please help Alexandra to find the minimal number of pieces meeting the condition above.

Input

The first line contains three space-separated integers *n*, *s*, *l* (1 ≤ *n* ≤ 10^{5}, 0 ≤ *s* ≤ 10^{9}, 1 ≤ *l* ≤ 10^{5}).

The second line contains *n* integers *a*_{i} separated by spaces ( - 10^{9} ≤ *a*_{i} ≤ 10^{9}).

Output

Output the minimal number of strip pieces.

If there are no ways to split the strip, output -1.

Examples

Input

7 2 2

1 3 1 2 4 1 2

Output

3

Input

7 2 2

1 100 1 100 1 100 1

Output

-1

Note

For the first sample, we can split the strip into 3 pieces: [1, 3, 1], [2, 4], [1, 2].

For the second sample, we can't let 1 and 100 be on the same piece, so no solution exists.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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