Question: What song was the title track of a movie in 1987 and then was covered by Dragon Ash more than 20 years later?

Context paragraphs:
Shizuka na Hibi no Kaidan o: "Shizuka na Hibi no Kaidan o" (静かな日々の階段を , Climbing the Stairs of Quiet Days ) is the sixth LP recording by Dragon Ash; released in 2000.  The title track was the ending theme for the popular Japanese film "Battle Royale", also released in 2000.  A version of the song appeared on their 2001 album Lily of da Valley.

Lily's E.P.: Lily's E.P. is the eighth maxi single by Dragon Ash; released in 2000.  It is stated on the CD packaging that both "Amploud" and "静かな日々の階段を" (Shizuka na Hibi no Kaidan o) are lead tracks, as opposed to the general trend in the music industry to dedicate singles to one lead or title track.

The Day Dragged On: The Day Dragged On is the first commercial release and first mini-album by Dragon Ash; released in 1997.  The song "天使ノロック (Tenshi no Rokku)" became a Buzz Clip (a song deemed popular enough to have its video placed on high rotation) on MTV Japan for one week.

Río de Emoción: Río de Emoción is the sixth full-length album by Dragon Ash; released in 2005.  It draws heavily on Spanish influences, with several of the tracks drawing influences from Latin music and instruments.  The title of the album is also Spanish for "River of Emotion".  The track "Resound ft. HIDE, 136" was featured in the 2006 movie .

Yume de Aetara (song): "Yume de Aetara" (official title: 夢で逢えたら) is the seventeenth maxi single by Dragon Ash; released in late 2006.  Like their previous two singles, this single was part of the countdown to Dragon Ash's tenth anniversary album Independiente released in 2007.

La Bamba (song): "La Bamba" has been covered by numerous artists, most notably by Los Lobos, whose version was the title track of the 1987 film "La Bamba" and reached No. 1 in the U.S. and UK singles charts in the same year.  The Los Lobos version remained No. 1 for three weeks in the summer of 1987.  The music video for Los Lobos' version, directed by Sherman Halsey, won the 1988 MTV Video Music Award for Best Video from a Film.

Hi wa Mata Noborikuri Kaesu: "Hi wa Mata Noborikuri Kaesu" (陽はまたのぼりくりかえす ) is the first maxi single by Japanese group Dragon Ash, released in 1998.  The single's title track was the opening theme to the 1998 anime DT Eightron.

Rainy Day and Day: "Rainy Day and Day" is the first single by the Japanese group Dragon Ash, which was released in 1997.  Their subsequent releases (not including full albums) were either maxi singles or LPs containing three or more tracks until the 2008 release of "Velvet Touch", which contains only the title track and B-Side "cover" "La Bamba".  The following single "Tsunagari Sunset" was also true to its name, with only the title track and B-side "Thought and Action".  However, 2009's "Unmei Kyōdōtai" saw a return to their maxi single releases.

Trois (album): Trois is the debut album by Japanese rock band Dustz, released on December 14, 2011.  The album's title is taken from the French word for the number three, as the band consists of three members who are fluent in three languages: Japanese, French, and English.  The album will feature the band's four major release singles "Break & Peace", "Brilliant Day", "Criez", and "spiral".  "Trois" will also include a cover of Dragon Ash's "Fantasista", with guest musicians Wes Borland and John Otto of Limp Bizkit.

Lily of da Valley: Lily of da Valley is the fourth full-length album by Dragon Ash; released in 2001.  The limited edition features "Episode 2 ft. SHUN, SHIGEO （Album Version）" as a bonus track.

Supporting paragraphs: Rainy Day and Day La Bamba (song)
Answer: "La Bamba"