403381: GYM101147 G The Galactic Olympics

Altanie is a very large and strange country in Mars. People of Mars ages a lot. Some of them live for thousands of centuries!

Your old friend Foki "The president of the Martian United States of Altanie" is the oldest man on Mars. He's very old no one knows how old he is! Foki loves children, so, he had (0 < K ≤ 10⁶) children!

The government in Altanie decided to send a team of athletes to Venus. To participate in (0 < N ≤ 10³) different game in the Galactic Olympics. So Foki told them to send his children instead!

Foki is in a big problem. How can he decide whom of his children is going to participate in which game, at the same time his children must participate in all the games and every one of his children get to participate in at least one game?

Note that in a certain arrangement, each one of Foki's children can participate in multiple games in the Olympics, but each game must be arranged to exactly one player.

Your job is to help Foki and answer his question: in how many way can he arrange his children to the games in Venus Olympics while satisfying the previous two conditions.

The first line of the input contains T the number of the test cases. Each test is represented with two integers on a single line. ( 0 < N ≤ 10³ ) the number of the games in the Olympics, ( 0 < K ≤ 10⁶ ) the number of Foki's children.

For each test case print one line contains the answer to Foki's question. Since the answer is very large. Print the answer modulo 10⁹ + 7

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