How to append a query string to pagination?

Refer this: Paginate Codex

I can see that you are using custom query so you put this below and outside the while loop

<?php
        global $wp_query;
        $big = 999999999; // need an unlikely integer
        $args = array(
            'base' => str_replace( $big, '%#%', esc_url( get_pagenum_link( $big ) ) ),
            'format' => '?page=%#%',
            'total' => $wp_query->max_num_pages,
            'current' => max( 1, get_query_var( 'paged') ),
            'show_all' => true,
            'end_size' => 1,
            'mid_size' => 2,
            'prev_next' => False,
            'prev_text' => __('&laquo; Previous'),
            'next_text' => __('Next &raquo;'),
            'type' => 'list',
            );
        echo paginate_links($args);
    ?>

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