Let's call an array a of size n coprime iff gcd(a₁, a₂, ..., a_n) = 1, where gcd is the greatest common divisor of the arguments.

You are given two numbers n and k. For each i (1 ≤ i ≤ k) you have to determine the number of coprime arrays a of size n such that for every j (1 ≤ j ≤ n) 1 ≤ a_j ≤ i. Since the answers can be very large, you have to calculate them modulo 10⁹ + 7.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 2·10⁶) — the size of the desired arrays and the maximum upper bound on elements, respectively.

Output

Since printing 2·10⁶ numbers may take a lot of time, you have to output the answer in such a way:

Let b_i be the number of coprime arrays with elements in range [1, i], taken modulo 10⁹ + 7. You have to print $\text{[math]}$ , taken modulo 10⁹ + 7. Here $\text{[math]}$ denotes bitwise xor operation (^ in C++ or Java, xor in Pascal).

Note

Explanation of the example:

Since the number of coprime arrays is large, we will list the arrays that are non-coprime, but contain only elements in range [1, i]:

For i = 1, the only array is coprime. b₁ = 1.

For i = 2, array [2, 2, 2] is not coprime. b₂ = 7.

For i = 3, arrays [2, 2, 2] and [3, 3, 3] are not coprime. b₃ = 25.

For i = 4, arrays [2, 2, 2], [3, 3, 3], [2, 2, 4], [2, 4, 2], [2, 4, 4], [4, 2, 2], [4, 2, 4], [4, 4, 2] and [4, 4, 4] are not coprime. b₄ = 55.

Coprime Arrays

Examples